SOLUTION: log2x=log3+log(x-4)

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Question 212957: log2x=log3+log(x-4)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
log%28%282x%29%29+=+log%28%283%29%29%2Blog%28%28x-4%29%29 Apply the "product rule" to the right side.
log%28%282x%29%29+=+log%28%283%2A%28x-4%29%29%29 Simplify the argument of the right side.
log%28%282x%29%29+=+log%28%283x-12%29%29 Apply the rule: Iflog%28%28M%29%29+=+log%28%28N%29%29 then M=N
2x+=+3x-12 Add 12 to both sides.
2x%2B12+=+3x Subtract 2x from both sides.
12+=+x or highlight%28x+=+12%29
Check:
log%28%282x%29%29+=+log%28%283%29%29%2Blog%28%28x-4%29%29 subsitute x = 12.
log%28%2824%29%29+=+log%28%283%29%29%2Blog%28%2812-4%29%29 Evaluate.
log%28%2824%29%29+=+log%28%283%29%29%2Blog%28%288%29%29
1.3802+=+0.4771%2B0.9031
1.3802+=+1.3802