Question

Expand the Logarthim Below.

Answer 1

\[\log_{3}7(2x-3)^{2} \]

Answer 2

first bring the exponent down with the rule\[\log x^a=a\log x\]

Answer 3

Ok

Answer 4

\[2\log_{3}7(2x-3) \]

Answer 5

good, now you can use\[\log(ab)=\log a +\log b\]

Answer 6

Woops!
Since the exponent isn't being applied to the entire contents of the log, we should probably apply that second rule first.

Answer 7

wait a minute not the whole thing is to the power

Answer 8

\[\Large\rm \log_{3}7(2x-3)^{2}=\log_37+\log_3(2x-3)^2\]Yah :) Apply that second rule that was mentioned, first.

Answer 9

oh i am dumb

Answer 10

ok so \[\log_{3}7+ 2\log_{3}(2x-3) \]

Answer 11

can we go further?

Answer 12

Yah that looks prettyyy fully expanded! :o

Answer 13

Nah, that should do it :D

Answer 14

Ok thanks.