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Logarithms
- Thread starter Albi
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Deleted member 4993
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Hint: 100 = 5^2 * 2^2 and use definition of logarithm that states:If log(5)2=x and log(5)3=y then how much is log(45)100 going to be
logx(y) = z \(\displaystyle \ \ \to \ \ \) x^(z) = y
Please show us what you have tried and exactly where you are stuck.
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Please share your work/thoughts about this problem.
Please do as the Great Khan of Khan asks and show us what you have done so far.
Some ideas that may help you think about this problem.
[MATH]log_5(2) = x \text { and} 100 = 2^2 * 5^2 \implies log_5(100) = WHAT?[/MATH]
What is the unique factorization of 45 into primes?
Some ideas that may help you think about this problem.
[MATH]log_5(2) = x \text { and} 100 = 2^2 * 5^2 \implies log_5(100) = WHAT?[/MATH]
What is the unique factorization of 45 into primes?
If [MATH]\log_5{2}=x\[MATH] and [MATH]\log_5{3}=y\[MATH] then how much is [MATH]\log_4_5{100}\[MATH] going to be?[/MATH][/MATH][/MATH][/MATH][/MATH][/MATH]
[MATH]log_5(100) \text {is gonna be} log_5(10)^2=2log_5(2*5) \implies 2+2x[/MATH] now what can I do?Please do as the Great Khan of Khan asks and show us what you have done so far.
Some ideas that may help you think about this problem.
[MATH]log_5(2) = x \text { and} 100 = 2^2 * 5^2 \implies log_5(100) = WHAT?[/MATH]
What is the unique factorization of 45 into primes?
Yeah it was and the prime factorization of 45 is 3*3*5Among the log laws that you learned was there one about change of base?
And what is the prime factorization of 45?
And what is the change of base formula?Yeah it was and the prime factorization of 45 is 3*3*5
You know what log5(100) is. So how do you go about finding what log45(100) is?
It is log(x)y =1/log(y)x. I found log(5)100 but I can't figure out log(45)100And what is the change of base formula?
You know what log5(100) is. So how do you go about finding what log45(100) is?
That is not the change of base rule: it is a very special case.
[MATH]log_p(t) = log_q(t) \div log_q(p).[/MATH]
Let's prove that
[MATH]r = log_p(t) \implies p^r = t \implies \\ log_q(p^r) = log_q(t) \implies \\ r * log_q(p) = log_q(t) \implies \\ r = log_q(t) \div log_q(p) \implies \\ log_p(t) = log_q(t) \div log_q(p).[/MATH]In your problem, what would be useful values for p and t?
EDIT: Now you can see why the Khan of Khans started with the definition of logarithms. The change of base rule comes directly from that definition. You do not NEED to memorize it. All you needed to do in this problem was to recognize that this is a change of base problem, derive the law, and figure out how to apply it.
[MATH]log_p(t) = log_q(t) \div log_q(p).[/MATH]
Let's prove that
[MATH]r = log_p(t) \implies p^r = t \implies \\ log_q(p^r) = log_q(t) \implies \\ r * log_q(p) = log_q(t) \implies \\ r = log_q(t) \div log_q(p) \implies \\ log_p(t) = log_q(t) \div log_q(p).[/MATH]In your problem, what would be useful values for p and t?
EDIT: Now you can see why the Khan of Khans started with the definition of logarithms. The change of base rule comes directly from that definition. You do not NEED to memorize it. All you needed to do in this problem was to recognize that this is a change of base problem, derive the law, and figure out how to apply it.
Yaaaaaas I found the solution I can't believe how this didn't came to my mind. log(45)100=log(5)100/log(5)45= 2x+2/1+2yThat is not the change of base rule: it is a very special case.
[MATH]log_p(t) = log_q(t) \div log_q(p).[/MATH]
Let's prove that
[MATH]r = log_p(t) \implies p^r = t \implies \\ log_q(p^r) = log_q(t) \implies \\ r * log_q(p) = log_q(t) \implies \\ r = log_q(t) \div log_q(p) \implies \\ log_p(t) = log_q(t) \div log_q(p).[/MATH]In your problem, what would be useful values for p and t?
EDIT: Now you can see why the Khan of Khans started with the definition of logarithms. The change of base rule comes directly from that definition. You do not NEED to memorize it. All you needed to do in this problem was to recognize that this is a change of base problem, derive the law, and figure out how to apply it.
Thanks for taking the time to help
log(45)100=log(5)100/log(5)45= 2x+2/1+2y
Your grouping symbols are in the wrong place or are missing. To show the use of
a logarithm base, I'll use "_" before it:
log_45(100) = [log_5(100)]/[log_5(45)] = (2x + 2)/(2y + 1)
or
\(\displaystyle log_{45}(100) \ = \ \dfrac{log_{5}(100)}{log_{5}(45)} \ = \ \dfrac{2x + 2}{2y + 1}\)
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