SOLUTION: How do you solve a log equations where there is x on both sides and one where there is only one x on one side? Such as the following? {{{ log ( 3, x )^2}}} ={{{ log( 3, 4 )}}}

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Question 30396: How do you solve a log equations where there is x on both sides and one where there is only one x on one side? Such as the following?
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Thank you very much!!!
Found 2 solutions by Paul, josmiceli:
Answer by Paul(988) (Show Source):
You can put this solution on YOUR website!
a) Since logarithm's bases are equal they can cancel out:

b)

Factor: (x+4) or (x-3)
x=-4 or x=3
Remove negative x =3
Paul.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
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I always say "logs are exponents" before I start with these
Then I think about what the equation says
The left side says there is an exponent (the right side) to
the base 3 that gives me x^2
3^(right side) = x^2

You have to say the left side to get it
The left side says "3 raised to the exponent to the base 3 that
gives me 4"
All that is just 4 if it gives me 4, so

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same thing
2^(right side) = (x+2)^2

same thing again
It says "raise 2 to an exponent to the base 2 that gives me 3x + 16"
That's just 3x + 16