Question

Expand the logarithmic expression.

log_b (sqrt)57/74

Answer 1

\[\log _{b}\sqrt{\frac{ 57 }{ 74 }}\]

Here, this looks a little nicer.

Answer 2

HI!!

Answer 3

write with exponents first \[\log_b\left(\frac{57}{74}\right)^{\frac{1}{2}}\]

Answer 4

Hullo ;w;
Ok!

Answer 5

then the one half comes out front since \[\log(x^n)=n\log(x)\]

Answer 6

one you do that, use the fact that \[\log(\frac{A}{B})=\log(A)-\log(B)\]

Answer 7

make sure to use parentheses, because the whole thing gets multiplied by one half

Answer 8

So, is it:

\[\frac{ 1 }{ 2 }\log _{b}57 - \frac{ 1 }{ 2 }\log_{b}74\]

or

\[\frac{ 1 }{ 2 }\log_{b}(57-74)\]
? Just to be sure

Answer 9

Sorry, Im super tired ;<;

Answer 10

first one

Answer 11

Thank you!

Answer 12

yw
btw the second one makes no sense
that would mean \[57\div 74=57-74\]

Answer 13

\[\color\magenta \heartsuit\]

Answer 14

Ah, ok. Thank you for explaining!