Question

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

log(10000x)

Answer 1

\[\log(10000x)=\log(10^{4}x)=\log(10^{4})+\log(x)=4+\log(x)\]

Answer 2

Okay and how would you do it for natural log like ln((e^11)/15))

Answer 3

\[\ln (\frac{ e ^{11} }{ 15 })=\ln(e ^{11})-\ln(15)=11\ln(e)-\ln(15)=11-\ln(15)\]

Answer 4

what about when square roots become a roll, like for the problem log_b((x^9sqrty)/z^3)

Answer 5

You mean

\[\log_{b}(\frac{ x ^{9}\sqrt{y} }{ z ^{3} } )\]

Answer 6

yeah!

Answer 7

\[\log_{b}(\frac{ x ^{9}\sqrt{y} }{ z ^{3} })=9\log_{b}x +\frac{ 1 }{ 2 }\log_{b}y-3\log_{b}z \]

Answer 8

this problem is step by step online so it has multiple parts. I understand that is the final answer but after step one I am suppose to fill in log_b(answer) - log_b(answer)

Answer 9

How about\[\frac{ 1 }{ 2 }\log_{b}x ^{18}y - 3\log_{b} z \] or\[\log_{b}x ^{9}y ^{\frac{ 1 }{ 2 }} -\log_{b}z ^{3}\]

Answer 10

Yes that was correct. Than after that answer it gives me

=log_b(answer)+log_b(answer)-log_b(answer)

Answer 11

Sorry It's chunked up until a bunch of steps I appreciate your help!!