If 2^x = 10, then how to calculate the value of 'x'?

2^3 = 8
2^4 = 16

It's in there, somewhere.

Have you considered a calculator?

Also, the important rule on the last question might be useful.

Please show your work.
 
2^3 = 8
2^4 = 16

It's in there, somewhere.

Have you considered a calculator?

Also, the important rule on the last question might be useful.

Please show your work.
No, I haven't.
I am unable to calculate. what will be the 'x' to get 10? how to start. I am confused.
 
No, I haven't.
I am unable to calculate. what will be the 'x' to get 10? how to start. I am confused.

Unless you use a calculator (specifically, the log button), you will have to use some method to approximate the answer, which could range from simple trial and error to various fancy numerical methods. This is not something for which there is a simple algebraic formula.

Can you tell us the context of your question? Why do you want to do this, and why do you not allow a calculator?
 
Unless you use a calculator (specifically, the log button), you will have to use some method to approximate the answer, which could range from simple trial and error to various fancy numerical methods. This is not something for which there is a simple algebraic formula.

Can you tell us the context of your question? Why do you want to do this, and why do you not allow a calculator?
Because the exam hall does not allow any type of calculators.
 
If 2^x = 10, here how to calculate the value of 'x'?
I'll be generous and show you how to do this 1st one.

Since 2^3=8 and 2^4=16 that trial and error method is not working.

Try taking log of both sides: log(2^x) = log10, but log(2^x) = x*log 2. So x*log 2 = log10. Now solve for x

My advice is to attend class AND listen
 
Because the exam hall does not allow any type of calculators.

Interesting. They assign problems that can't be solved efficiently without a calculator, then don't allow calculators? And they also don't teach you any method for solving this?

Are you perhaps allowed to use a logarithm table? Or might you be allowed to give an expression, rather than a number, as the answer?

Please give us more information about what you ARE allowed to do, and what you HAVE been taught about this kind of problem. Are you sure it is required on this exam? If so, what precision is required?
 
Interesting. They assign problems that can't be solved efficiently without a calculator, then don't allow calculators? And they also don't teach you any method for solving this?

Are you perhaps allowed to use a logarithm table? Or might you be allowed to give an expression, rather than a number, as the answer?

Please give us more information about what you ARE allowed to do, and what you HAVE been taught about this kind of problem. Are you sure it is required on this exam? If so, what precision is required?
What expression are you speaking of? The answer ix x= log10/log2 or x=1/log2 which I got in an efficient way and I did NOT use a calculator.

Are you suggesting that 1/log2 is not a number but rather an expression??
 
What expression are you speaking of? The answer is x= log10/log2 or x=1/log2 which I got in an efficient way and I did NOT use a calculator.

Are you suggesting that 1/log2 is not a number but rather an expression??

Yes, of course.

Normally, when someone asks for "the value of x", he is asking for a numerical value. I am hoping that your answer is what would be required, but that is not at all clear from the original question, or from Indranil's response, "I am unable to calculate. what will be the 'x' to get 10?".
 
Yes, of course.

Normally, when someone asks for "the value of x", he is asking for a numerical value. I am hoping that your answer is what would be required, but that is not at all clear from the original question, or from Indranil's response, "I am unable to calculate. what will be the 'x' to get 10?".
Strange, since I can calculate the the exact value of x. I can even check it

2^(1/log2)=2^(log210)=10. So what is the problem?

You really need to learn what an expression is.

1/log2 IS a real number! Just because it is not a friendly looking number does not mean it is not a real number. Is sqrt(7) a real number? How about pi??
 
Strange, since I can calculate the the exact value of x. I can even check it

2^(1/log2)=2^(log210)=10. So what is the problem?

You really need to learn what an expression is.

1/log2 IS a real number! Just because it is not a friendly looking number does not mean it is not a real number. Is sqrt(7) a real number? How about pi??

''2^(1/log2)=2^(log210)=10'' here could you explain how did you find 2^(1/log2) to (log210)?
 
If 2^x = 10, here how to calculate the value of 'x'?

Indranil, we need you to clarify what you were asking for. My understanding is that you were trying to calculate a specific numerical value, namely 3.3219280948873623478703194294894..., since you used words like "calculate" and "value". Others think that an expression representing that number is sufficient. Similarly, some algebra problems would ask explicitly for a numerical value (accurate to some number of decimal places) where others might ask for an exact value, so that they would want an expression like \(\displaystyle \sqrt{2}\). But this is not normally called a calculated value.

In order to know whether we have answered your question, it is important that you tell us what kind of answer is expected. On this exam, is an expression involving the logarithm function acceptable, or would you need a decimal value? What is the exact wording of the problem, and any instructions given with it?
 
My question is how is it possible
''2^(1/log2)=2^(log210)=10'' Could anyone explain here please?

A key idea here would be the change of base formula, which implies that log2(10) = log10(10)/log10(2) = 1/log10(2). That explains the first equality. Can you understand the second?
 
Indranil, we need you to clarify what you were asking for. My understanding is that you were trying to calculate a specific numerical value, namely 3.3219280948873623478703194294894..., since you used words like "calculate" and "value". Others think that an expression representing that number is sufficient. Similarly, some algebra problems would ask explicitly for a numerical value (accurate to some number of decimal places) where others might ask for an exact value, so that they would want an expression like \(\displaystyle \sqrt{2}\). But this is not normally called a calculated value.

In order to know whether we have answered your question, it is important that you tell us what kind of answer is expected. On this exam, is an expression involving the logarithm function acceptable, or would you need a decimal value? What is the exact wording of the problem, and any instructions given with it?
No no, that is the point, 3.3219280948873623478703194294894... is NOT a specific number. It is an approximation, and a good one, to 1/log2.

For example, sqrt(7) is 'the expression' for a number that when you multiply it by itself yields 7. Again, sqrt(7) is in fact a number, not an expression (although you never said it is an expression).

Now consider log27 for example. log27 represents the number that you raise 2 to, to get 7.

Please understand that 15 is a symbol for the number fifteen, just like log27 is the symbol of the number that you raise 2 to, to get 7.

For the record, NEVER in my entire life have I seen a 3! Absolutely never. And I don't expect to ever see one in my lifetime. If anyone has, then please go see a mathematician/eye doctor and I'm sure they will try to help. I have seen, countless time, the symbol for three (denoted by 3), but I have never seen a 3!
 
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My question is how is it possible
''2^(1/log2)=2^(log210)=10'' Could anyone explain here please?
Dr Peterson explained the 1st equality. For the 2nd, we have a theorem that statesa^logaX = X, for any a>0.
 
No no, that is the point, 3.3219280948873623478703194294894... is NOT a specific number. It is an approximation, and a good one, to 1/log2.

For example, sqrt(7) is 'the expression' for a number that when you multiply it by itself yields 7. Again, sqrt(7) is in fact a number, not an expression (although you never said it is an expression).

Now consider log27 for example. log27 represents the number that you raise 2 to, to get 7.

Please understand that 15 is a symbol for the number fifteen, just like log27 is the symbol of the number that you raise 2 to, to get 7.

For the record, NEVER in my entire life have I seen a 3! Absolutely never. And I don't expect to ever see one in my lifetime. If anyone has, then please go see a mathematician/eye doctor and I'm sure they will try to help. I have seen, countless time, the symbol for three (denoted by 3), but I have never seen a 3!

Jomo, I am not talking to you. I am not arguing about semantics or what a number is. You don't need to talk down to me as if I don't understand these things.

I am just trying to find out what kind of answer the OP needs, in order to be helpful. Can you let me do that?
 
Jomo, I am not talking to you. I am not arguing about semantics or what a number is. You don't need to talk down to me as if I don't understand these things.

I am just trying to find out what kind of answer the OP needs, in order to be helpful. Can you let me do that?
But it is obvious what the OP wanted. She/He wanted the solution, which might be irrational.
 
... a theorem that states

a^logaX = X, for any a>0.

On the left-hand side of the equation, the "x" should not be as low as it is. It should on the same level as "log."

a^\(\displaystyle log_ax \ = \ x. \)\(\displaystyle \ \ \ \)Also, \(\displaystyle \ a \ne 1, \) as well as a > 0.
 
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