Basic logarithm question

[vinayinvicible]

I was trying to solve a question and I got the solution by a method.

When I was solving this question by another method, I ended up with a strange result.

In the question it is given that

Now dividing these two equations we get

Since bases are different exponents must be equal to zero

So, we get

.

As we can see obviously this result is wrong as a and b values must be positive.

So, where have I gone wrong??

 

[Quaid]

I was trying to solve a question and I got the solution by a method.

When I was solving this question by another method, I ended up with a strange result.

In the question it is given that

Hi vinayinvicible:

What is the actual question? Did they simply state those two equations and then ask you to determine the value of symbols a and b?

What solution did you get, from your first attempt?

Now dividing these two equations we get

Since bases are different, exponents must be equal to zero

So, we get

.

I'm not sure how you arrived at -3 and -2, from the work that you posted, but the statement in red is not true; here are rounded approximates for those exponents.

1-b+a = 0.908005499

3b-2a = 1.439154666


If I were asked to determine a and b, I would use the change-of-base formula (for exact representations) and a scientific calculator (to evaluate for decimal approximations).

\(\displaystyle log_b(A) = \dfrac{ln(A)}{ln(b)}\)

Cheers

PS: When typing math expressions, it is much more understandable to show multiplication with an asterisk instead of a period.

That is, type 3*2^2 instead of 3.2^2

 

[HallsofIvy]

I was trying to solve a question and I got the solution by a method.

When I was solving this question by another method, I ended up with a strange result.

In the question it is given that

Now dividing these two equations we get

Since bases are different exponents must be equal to zero

This is certainly NOT true. For example, \(\displaystyle 3^{\frac{ln(2)}{ln(3)}}= 2^1\)

So, we get

.

As we can see obviously this result is wrong as a and b values must be positive.

So, where have I gone wrong??

 

[vinayinvicible]

Thank you guys.

I understood my mistake.

That was the dumbest thing I have ever done.