Question

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

Answer 1

you would use the rule

log(A/B) = log(A) - log(B)

Answer 2

and this rule as well

log(A^B) = B*log(A)

Answer 3

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

Answer 4

ignore the x > 6 part

Answer 5

that doesn't need to be written again

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

okay so that will be the simplified form

Answer 11

yes

Answer 12

thank you!

Answer 13

yw

Answer 14

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