SOLUTION: solve: log(2x-3)-(logx-log8)=1

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Question 1008009: solve: log(2x-3)-(logx-log8)=1
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%282x-3%29%29-%28log%28%28x%29%29%5E%22%22-log%28%288%29%29%29%22%22=%22%221

Remove the large parentheses

log%28%282x-3%29%29-log%28%28x%29%29%2Blog%28%288%29%29%22%22=%22%221

On the first two terms, use the principle 

                log%28%28a%29%29-log%28%28b%29%29=log%28%28a%2Fb%29%29

log%28%28%282x-3%29%2Fx%29%29%2Blog%28%288%29%29%22%22=%22%221

On the two terms on the left, use the principle 

                log%28%28a%29%29%2Blog%28%28b%29%29=log%28%28a%2Ab%29%29

log%28%28+++%28++%282x-3%29%2Fx++%29%5E%22%22%2A%288%29%5E%22%22+++++%29%29%22%22=%22%221

Write 8 as 8%2F1

log%28%28+++%28++%282x-3%29%2Fx++%29%5E%22%22%2A%288%2F1%29%5E%22%22+++++%29%29%22%22=%22%221

Multiply numerators and denominators:

log%28%28++%2816x-24%29%2Fx++++++++%29%29%22%22=%22%221

When the base of a log isn't written it is understood
to be 10

log%2810%2C%28++%2816x-24%29%2Fx++++++++%29%29%22%22=%22%221

Use the principle that the log equation
           log%28b%2C%28a%29%29=c can be written as the exponential
           equation a=b%5Ec

%2816x-24%29%2Fx%22%22=%22%2210%5E1

%2816x-24%29%2Fx%22%22=%22%2210

Multiply both sides by x

16x-24%22%22=%22%2210x

6x-24%22%22=%22%220

6x%22%22=%22%2224

x%22%22=%22%224

Edwin