Question

how to do log base 16 of 1/4 ?!?!?!?!

Answer 1

\[\log_{16}\frac{1}{4}=x \rightarrow 16^x=4^{-1}\]Put them in the same base:\[4^{2x}=4^{-1}\]
\[2x=-1\rightarrow x=-\frac{1}{2}\]

Answer 2

or use change of base formula...
\[\log_{16} \left(\frac{1}{4}\right) = \frac{\log 0.25}{\log 16}\]

Answer 3

then what would i do how do you divide them?

Answer 4

or if i use what ivanmlerner did what would i do next?

Answer 5

For the change of base formula, just use a calculator with a log key:
log(0.25)/log(16) =

Answer 6

but i can't use a calculator

Answer 7

what if i did it how ivanmlerner did it?

Answer 8

if you do it the way @ivanmlerner suggested, then you are done. By finding x, you found the value of the log, that is
\[\log_{16} \left(\frac{1}{4}\right) = -\frac{1}{2}\]

Answer 9

wait so x is -1/2

Answer 10

how did you get -1/2

Answer 11

wait nevermind i got it

Answer 12

wait so what about something like log base 1/4 of 16?

Answer 13

you would go about it the same way, basically.

Asking what \(\log_{1/4} 16\) is equal to is the same as asking the question "what power do I raise \(\dfrac{1}{4}\) to to get \(16\)?"

In math, that means solving the equation for x:
\[\large \left(\frac{1}{4}\right)^x = 16\]

Answer 14

so 64?