Question

Can someone help me evaluate this logarithmic expression?

Answer 1

write \(\frac{1}{32}\) as a power of \(2\) i.e. write \(\frac{1}{32}=2^n\) for some \(n\) (it will be negative)
then your answer is \(n\) as what you are trying to solve in exponential form is
\[2^n=\frac{1}{32}\]

Answer 2

Do I not need to break them down to the same base number?

Answer 3

@satellite73

Answer 4

i am not sure what "them" means in this context
in inequivalent exponential form
\[\log_2(\frac{1}{3})=x\iff 2^x=\frac{1}{32}\] you are looking for \(x\) the number you would raise 2 to the power of to get \(\frac{1}{32}\)

Answer 5

typo there, i meant
\[\log_2(\frac{1}{32})=x\iff 2^x=\frac{1}{32}\]

Answer 6

I got -5. Is that correct?

Answer 7

@satellite73