Question

Expand the logarithmic expression
logb square root of 13/74

1. 1/2 logb 13 - 1/2logb 73
2. 1/2 logb 13 + 1/2logb 73
3. logb (13-73)
4. sqrt logb (13-73)

Answer 1

\[\log_b(\sqrt{\frac{13}{17}})\]?

Answer 2

no 13/74

Answer 3

\[\log_b\left(\sqrt{\frac{13}{73}}\right)\] like that?

Answer 4

haha yes that's it

Answer 5

first rewrite the radical in exponential notation as \[\log_b\left({\frac{13}{73}}\right)^{\frac{1}{2}}\] then the \(\frac{1}{2}\) comes out front as
\[\frac{1}{2}\log_b(\frac{13}{73})\]

Answer 6

after that use \(\log(\frac{A}{B})=\log(A)-\log(B)\) to give you
\[\frac{1}{2}\left(\log_b(13)-\log_b(73)\right)\]

Answer 7

and finally distribute the \(\frac{1}{2}\)

Answer 8

so, 1/2 logb 13- 1/2logb 73?