Question

log(8)a/2
expand the logarithmic expression

Answer 1

Can someone tell me if Im doing this right?
log(8)(a/2)=log(8)(ax)-log(8)(2)
log(8)(a)+log(8)(x)-log(8)(2)
answer= log(8)a-log(8)2

Answer 2

@zepdrix

Answer 3

I don't understand where the x came from. I don't see an x in the original problem.
Since you're offline, I'll just have to guess at what's going on :D lol
\[\huge \log_8 \left(\frac{a}{2}\right)\]Here is a familiar log rule,\[\huge \log a - \log b = \log \left(\frac{a}{b}\right)\]We are basically applying this rule in reverse.\[\large \log_8 \left(\frac{a}{2}\right)\quad = \quad \huge \color{purple}{\log_8(a)-\log_8(2)}\]

Answer 4

It looks like you got the right answer, so that's good. I just can't quite understand your steps.

Answer 5

If the problem was suppose to be THIS,\[\huge \log_8 \left(\frac{ax}{2}\right)\]Then we need to apply another log rule,\[\huge \log a + \log b=\log(ab)\]Which from where we last left off here,\[\huge \color{black}{\log_8(a\color{red}{x})-\log_8(2)}\]Would expand to,\[\huge \color{black}{\log_8(a)\color{red}{+\log_8(x)}-\log_8(2)}\]