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

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Question 110929: solve exactly
log(x+4)-log(x-3)=log 8
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%28x%2B4%29%29-log%2810%2C%28x-3%29%29=log%2810%2C%288%29%29 Start with the given equation


log%2810%2C%28%28x%2B4%29%2F%28x-3%29%29%29=log%2810%2C%288%29%29 Combine the logs using the identity log%28a%29-log%28b%29=log%28a%2Fb%29


%28x%2B4%29%2F%28x-3%29=8 Since the bases are equal, the arguments are equal


x%2B4=8%28x-3%29 Multiply both sides by x-3


x%2B4=8x-24 Distribute



x=8x-24-4Subtract 4 from both sides


x-8x=-24-4 Subtract 8x from both sides


-7x=-24-4 Combine like terms on the left side


-7x=-28 Combine like terms on the right side


x=%28-28%29%2F%28-7%29 Divide both sides by -7 to isolate x



x=4 Divide

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Answer:
So our answer is x=4

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%2B4%29%29-log%28%28x-3%29%29=log+%28%288%29%29........... apply rule log%0D%0A%0D%0A%28%28a%2Fb%29%29+=+log%28%28a%29%29-log%28%28b%29%29
log%28%28%28x%2B4%29%2F%28+x-3%29%29%29=log+%288%29... notice that bases are same, and if
log+b%28%28x%29%29=+log+b+%28%28y%29%29, then +x+=+y; it means we can write:
%28x%2B4%29%2F%28+x-3%29=+8... multiply both sides by x-3
%28%28x%2B4%29%2F%28+x-3%29%29%28x-3%29=+8%28x-3%29... cancel both x-3 on the left
side and multiply by 8 on the right side
x%2B4=+8x+%96+24......move x to the right and -24 to the left
4++%2B+24+=+8x+%96+x......
28+=+7x+......divide both sides by 7
4+=+x+......or
x++=+4+