SOLUTION: {{{log(x+5)-log(x+2)=log5}}}

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Question 132628: log%28x%2B5%29-log%28x%2B2%29=log5
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%28x%2B5%29%29-log%2810%2C%28x%2B2%29%29=log%2810%2C%285%29%29 Start with the given equation



log%2810%2C%28%28x%2B5%29%2F%28x%2B2%29%29=log%2810%2C%285%29%29%29 Combine the logs using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29



Raise both sides as exponents with bases of 10. This will undo the logs


%28x%2B5%29%2F%28x%2B2%29=5 Simplify


x%2B5=5%28x%2B2%29 Multiply both sides by x%2B2


x%2B5=5x%2B10 Distribute


x=5x%2B10-5Subtract 5 from both sides


x-5x=10-5 Subtract 5x from both sides


-4x=10-5 Combine like terms on the left side


-4x=5 Combine like terms on the right side


x=%285%29%2F%28-4%29 Divide both sides by -4 to isolate x



x=-5%2F4 Reduce

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Answer:
So our answer is x=-5%2F4 (which is approximately x=-1.25 in decimal form)