1
$\begingroup$

$$\log({ \log }_{ 10 }10000)$$

Steps I took to solve this:

${ \log }_{ 10 }10000=4$

${ \log }_{ 10 }4=y$

$10^{ y }=4$

${ \log }10^{ y }=\log 4$

$y=\frac { \log 4 }{ \log 10 } $

doesn't seem to come out to the correct answer...

$\endgroup$
3
  • 1
    $\begingroup$ Note that $\log 10 = 1$. $\endgroup$
    – E W H Lee
    Sep 28, 2014 at 2:47
  • $\begingroup$ yes, so when I evaluate it one step further, it goes back to equaling $log4$ and $log4$ is not the correct answer $\endgroup$ Sep 28, 2014 at 2:49
  • $\begingroup$ It is correct; you can test it with your calculator. $\endgroup$
    – E W H Lee
    Sep 28, 2014 at 2:50

3 Answers 3

1
$\begingroup$

Your answer is correct since $$\log (\log (10000)) = \log (\log (10^4)) = \log(4\log(10)) = \log 4$$

$\endgroup$
3
  • $\begingroup$ why does the answer key state $4$ is the answer then? $\endgroup$ Sep 28, 2014 at 2:50
  • $\begingroup$ Either a mistake in the book or you misunderstood the question? $\endgroup$
    – E W H Lee
    Sep 28, 2014 at 2:52
  • $\begingroup$ The book must be wrong. $\endgroup$ Sep 28, 2014 at 2:58
1
$\begingroup$

$y=\log_{10}4=\frac{\log 4}{\log 10}=\log 4$

$\endgroup$
1
$\begingroup$

$\log({ \log }_{ 10 }10000)$

$=\log_{10} ( \log_{10} 10^4)$

$=\log_{10} (4 \log_{10} 10)$

$=\log_{10}4$

Yours is correct.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.