Author Topic: Logs and exponential functions (Read 1761 times) Tweet Share

RL989 · « **on:** May 06, 2018, 02:47:43 pm »

Hi, could someone explain how to solve the following question:

If f(x) = 3loge (2x) , and f(5x) = loge (y), then find the value of y.

[ANSWER: 1000x^3]

thanks

RuiAce · « **Reply #1 on:** May 06, 2018, 02:51:14 pm »

Quote from: RL989 on May 06, 2018, 02:47:43 pm

Hi, could someone explain how to solve the following question:

If f(x) = 3loge (2x) , and f(5x) = loge (y), then find the value of y.

[ANSWER: 1000x^3]

thanks

$\text{If by definition }f(x) = 3\log_e 2x\\ \text{then }\boxed{f(5x) = 3\log_e 10x}.$
$\text{But we're }\textbf{also}\text{ told that }f(5x) = \log_e y.\\ \text{So upon equating, }\boxed{3\log_e 10x = \log_e y}.$
$\text{Using relevant log laws, this equation rearranges to give}\\ \begin{align*}\log_e (10x)^3 &= \log_e y\\ (10x)^3 &= y\\ 1000x^3 &= y\end{align*}$

RL989 · « **Reply #2 on:** May 06, 2018, 03:12:40 pm »

Thank you so much!

RL989 · « **Reply #3 on:** May 06, 2018, 04:34:18 pm »

Hello again,
could I also get some help with the following ques:

Correct answer is B

KT Nyunt · « **Reply #4 on:** May 06, 2018, 06:38:39 pm »

Quote from: RL989 on May 06, 2018, 04:34:18 pm

Hello again,
could I also get some help with the following ques:

Correct answer is B

This is an application of the change of base rule: (see attachment)

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Author Topic: Logs and exponential functions (Read 1761 times) Tweet Share

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Logs and exponential functions

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