SOLUTION: Solve for x: 2logx=log2+log(3x-4)

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Question 131546This question is from textbook
: Solve for x:
2logx=log2+log(3x-4) This question is from textbook

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for x: 
2%2Alog%28%28x%29%29=log%28%282%29%29%2Blog%28%283x-4%29%29

Use this rule of exponents on the left side

                     A%2Alog%28%28B%29%29=log%28%28B%5EA%29%29

log%28%28x%5E2%29%29=log%28%282%29%29%2Blog%28%283x-4%29%29

Use this rule of logarithms on the right side:

                     log%28%28A%29%29+%2B+log%28%28B%29%29+=+log%28%28AB%29%29 

log%28%28x%5E2%29%29=log%28%282%283x-4%29%29%29

Distribute on the right:

log%28%28x%5E2%29%29=log%28%286x-8%29%29%29

Use the rule:

               The equation log%28%28A%29%29 = log%28%28B%29%29 is equivalent to
               the equation A=B

x%5E2=6x-8

x%5E2-6x%2B8=0

%28x-2%29%28x-4%29=0

x-2=0 gives solution x=2

x-4=0 gives solution x=4
                        
Edwin