SOLUTION: can you please explain this to me step by step so i can understand it. log(3-2x) - log (x+9)=0 i hope you can help me understand this thank you julie

Question 119567: can you please explain this to me step by step so i can understand it.
log(3-2x) - log (x+9)=0
i hope you can help me understand this
thank you
julie
Found 2 solutions by jim_thompson5910, MaxLiebling:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation. Note: Since you did not specify a base, this means that we're going to use the default base 10.

Combine the logs using the identity

Rewrite the equation using the property: ====>

Evaluate to get

Multiply both sides by

Subtract 9 from both sides

Add 2x to both sides

Combine like terms on the left side

Combine like terms on the right side

Divide both sides by 3 to isolate x

Divide

--------------------------------------------------------------
Answer:
So our answer is

Answer by MaxLiebling(13) (Show Source): You can put this solution on YOUR website!
Start with the given equation:

add to both sides:

Note: logarithm is a strictly increasing function AND on both sides you have nothing but a Log(...) -> drop Log:

add to both sides:

calculate left side:
= = =
calculate right side:
= = =
combine both sides:
=
that is:

divide both sides by 3:

calculate =

proof left hand side:
= = = = =
proof right hand side:
= = =
both sides are equal:
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