Question

Logarthim help?> (PIC INSERTED)

Answer 1

put both logs on one side, and \(1\) on the other as a start

Answer 2

on one side?

Answer 3

\[\log_5(x+3)+\log_5(x+7)=1\]

Answer 4

i guess what i meant was put all the logs on the left, the number on the right

Answer 5

I forgot how to do logs. i dont know what to do with bases.

Answer 6

now combine in to a single log using \(\log(A)+\log(B)=\log(AB)\)

Answer 7

we are not there yet,
next step is to write
\[\log_5((x+3)(x+7))=1\]

Answer 8

ok

Answer 9

finally we use the definition of a logarithm to rewrite in equivalent exponential form
\[\log_b(x)=y\iff x=b^y\]

Answer 10

since your base is \(5\) you get
\[(x+7)(x+3)=5^1\] or simply
\[(x+3)(x+7)=5\]

Answer 11

since 1 is the exponent i can jus leave it as 5

Answer 12

yes

Answer 13

is that the answer or are there more solutions @satellite73

Answer 14

now you get to solve a quadratic equation
enjoy

Answer 15

what?

Answer 16

oh no, that is the answer to nothing, that is a step along the way
you have to solve
\[(x+3)(x+7)=5\] for \(x\)

Answer 17

your job is to find \(x\)

Answer 18

do i FOIL?

Answer 19

that is a first step in solving the quadratic, yes

Answer 20

im going to foil it now but what do i do after? @satellite73

Answer 21

subtract 5 to set it equal to zero, then see if you can factor it