Question

solve the following log equation
question below

Answer 1

\[\log_{3}x+\log_{3}(x-8)=2 \]

Answer 2

the first step is use the rule
\[ \log(a)+\log(b)= \log(a\cdot b) \]
in other words, you can replace the addition of two logs (of the same base)
with one log, where you multiply.

can you do that ?

Answer 3

yea i got that so far

Answer 4

what do you have so far ?

Answer 5

x^2-8x inside log

Answer 6

\[ \log_3(x^2-8x) = 2\]

make each side the exponent of the base 3:
\[ 3^{\log_3(x^2-8x)} = 3^2\]

and use the rule
\[ a^{log_a(b)} = b \]
to simplify the left side. in other words, 3 to the power log base 3 "undoes" the log

Answer 7

do you end up with just x^2-8x=9

Answer 8

yes

Answer 9

ok cool then factor and x=-1 cant be in the solution so its just 9

Answer 10

yes