SOLUTION: solve exactly log(x+4)-log(x-3)=log 8

Question 110929: solve exactly
log(x+4)-log(x-3)=log 8
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Combine the logs using the identity

Since the bases are equal, the arguments are equal

Multiply both sides by x-3

Distribute

Subtract 4 from both sides

Subtract 8x from both sides

Combine like terms on the left side

Combine like terms on the right side

Divide both sides by -7 to isolate x

Divide

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Answer:
So our answer is
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
........... apply rule
... notice that bases are same, and if
, then ; it means we can write:
... multiply both sides by
... cancel both on the left
side and multiply by on the right side
......move to the right and to the left
......
......divide both sides by
......or

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