write expression as a sum or difference of logarithms. express power as factors.
log base 5 ((x^6)/(x-6)) x 6

Question

write expression as a sum or difference of logarithms. express power as factors.
log base 5 ((x^6)/(x-6)) x >6

jim_thompson5910 · Answer

you would use the rule

log(A/B) = log(A) - log(B)

jim_thompson5910 · Answer

and this rule as well

log(A^B) = B*log(A)

anonymous · Answer

okay so it will look like log (base5)(x^6)-log (base5)(x-6) (x)>6

jim_thompson5910 · Answer

ignore the x > 6 part

jim_thompson5910 · Answer

that doesn't need to be written again

jim_thompson5910 · Answer

it's just there to guarantee that the expression (x^6)/(x-6) is always positive

jim_thompson5910 · Answer

after getting that, use the rule log(A^B) = B*log(A)

anonymous · Answer

so it will look like (6log(x))-log(x-6)

jim_thompson5910 · Answer

good, each log is assumed to be base 5, but no need to write "base 5" for each log if you make that statement

anonymous · Answer

okay so that will be the simplified form

jim_thompson5910 · Answer

yes

anonymous · Answer

thank you!

jim_thompson5910 · Answer

yw

anonymous · Answer