Question

express as a single logarithm:
\[\frac{ 1 }{ 2 } [(\log_{5} a+2\log_{5}b)-3\log_{5}c] \]

Answer 1

Just use the following rules:\[
a\log(b) = \log(b^a)
\quad \quad
\log(a)+\log(b) = \log(ab)
\]

Answer 2

@wio which i did... but idk what steps im doing wrong... or what im not doing.. /:

Answer 3

Okay well type your steps out and I'll tell you if they're good

Answer 4

\[1/2 [\log_{5}ab^{2} - 3\log_{5}c]\]\[1/2[\frac{ \log_{5}ab ^{2} }{ \log_{5}c ^{3} } ]\]

Answer 5

then what do i do from there...

Answer 6

@wio

Answer 7

ohp... nvmm -.- i got \[\log_{5}\frac{ (b \sqrt{a} ) }{ c ^3}\]

Answer 8

Ummmm

that square root should be applied to the c as well.

Answer 9

so... then it should be... ? :S

Answer 10

\[ \Large
\log_5\left(\sqrt{\frac{ab^2}{c^3}}\right) = \log_5\left(\frac{|b|\sqrt{ac^3}}{c^3}\right)
\]

Answer 11

We can probably assume that \(b > 0 \implies |b| = b\) though, since otherwise \(2\log_5(b)\) would be undefined.

Answer 12

uhh... would that mean the answer at the back is wrong then? cause what i got was what it says in the back of the worksheet... :S

Answer 13

Ummm, you should take the square root of that \(c^3\) at some point.