SOLUTION: find x -3log(x+2)+log5=0 The answer is -2+cube root of 5 What steps are involved in getting to that answer?

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Question 147145: find x
-3log(x+2)+log5=0
The answer is -2+cube root of 5
What steps are involved in getting to that answer?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-3log%2810%2C%28x%2B2%29%29%2Blog%2810%2C%285%29%29=0 Start with the given equation


-3log%2810%2C%28x%2B2%29%29=-log%2810%2C%285%29%29 Subtract log%2810%2C%285%29%29 from both sides.


log%2810%2C%28x%2B2%29%5E%28-3%29%29=-log%2810%2C%285%29%29 Rewrite the left side using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


log%2810%2C%28x%2B2%29%5E%28-3%29%29=log%2810%2C%285%29%5E%28-1%29%29 Rewrite the right side using the identity y%2Alog%28b%2C%28x%29%29=log%28b%2C%28x%5Ey%29%29


%28x%2B2%29%5E%28-3%29=%285%29%5E%28-1%29 Since the logs are equal with the same base, this means that arguments are equal


1%2F%28x%2B2%29%5E%283%29=1%2F%285%29%5E%281%29 Flip the fractions


5%5E1=%28x%2B2%29%5E%283%29 Cross multiply.


5=%28x%2B2%29%5E%283%29 Simplify.


root%283%2C5%29=x%2B2 Take the cube root of both sides.


root%283%2C5%29-2=x Subtract 2 from both sides.


-2%2Broot%283%2C5%29=x Rearrange the terms.



So the answer is x=-2%2Broot%283%2C5%29