Question

log base 16 of 49 - log base 4 of 7. Explain

Answer 1

Use the change of base formula to simplify this

Answer 2

\[(\log49/\log16)-(\log7/\log4)\]
Then what?

Answer 3

You have to use change of base formula appropriately to simplify this.

Hint:
\[\log_{7} 7^2 = 2\]

Answer 4

But there are no bases that work with 49 and 16 or 7 and 4. You're left with: \[\log_{4}49/2 - \log_{2}7/4 \]

Answer 5

\[\frac{\log_4{49}}{\log_4{4^2}} = \frac{1}{2}\log_4{49}\]

Now you have:

\(\dfrac{1}{2}\log_4{7^2} - \log_4{7} = \dfrac{2}{2}\log_4{7} - \log_4{7} \)

\( = 0\)

Answer 6

Do you get it now?

Answer 7

Sort of... The general sense. Thanks.

Answer 8

All set!