SOLUTION: log10 (x + 6) - log10 (x - 6) = 1 Find x in the following equation Homework question from Hans

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Question 1176150: log10 (x + 6) - log10 (x - 6) = 1
Find x in the following equation



Homework question from Hans

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Use rules of logarithms to write the left hand side as a single logarithm.



log%2810%2C%28%28x%2B6%29%2F%28x-6%29%29%29+=+1

(2) Convert the logarithmic equation to exponential form.

%28x%2B6%29%2F%28x-6%29+=+10%5E1+=+10

(3) Solve the resulting equation.

%28x%2B6%29+=+10%28x-6%29
x%2B6+=+10x-60
66+=+9x
x+=+66%2F9+=+22%2F3

ANSWER: x = 22/3