Question

Solve for x

Answer 1

\[3^{4x} = 13 ^{-x +7}\] use base-10 logarithms

Answer 2

take log of both sides

\(\log_{10}(3^{4x})=\log_{10}(13^{-x+7})\\4x\log_{10}(3)=(-x+7)\log_{10}(13)\)

Answer 3

you with me?

Answer 4

okay I am following

Answer 5

can you solve for x?

Answer 6

distribute the log(13) on the right

Answer 7

then add xlog(13) to both sides

Answer 8

factor out the x on the left
divide to get x alone

Answer 9

in that order:)

Answer 10

um let me try.

Answer 11

k

Answer 12

Okay, I am stuck on distributing logs.

Answer 13

do it as you would a number

Answer 14

(a+b)c = ac+bc

Answer 15

here c = log(13)

Answer 16

\(\log_{10}(3^{4x})=\log_{10}(13^{-x+7})\\4x\log_{10}(3)=(-x+7)\log_{10}(13)\\4x\log_{10}(3)=-x\log_{10}(13)+7\log_{10}(13)\)

Answer 17

\(\log_{10}(3^{4x})=\log_{10}(13^{-x+7})\\4x\log_{10}(3)=(-x+7)\log_{10}(13)\\4x\log_{10}(3)=-x\log_{10}(13)+7\log_{10}(13)\\4x\log_{10}(3)+x\log_{10}(13)=7\log_{10}(13)\\x(4\log_{10}(3)+\log_{10}(13))=7\log_{10}(13)\\x=\frac{7\log_{10}(13)}{4\log_{10}(3)+\log_{10}(13)}\)

Answer 18

okay, let me see if I understand it.