SOLUTION: Solve for x log_4 (3x+1) = log_2 (x-1) *** Log_4 = log to base 4

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Question 923816: Solve for x
log_4 (3x+1) = log_2 (x-1)
***
Log_4 = log to base 4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%284%2C%283x%2B1%29%29+=+log%282%2C%28x-1%29%29 ...change to base 10

log%28%283x%2B1%29%29%2Flog%284%29+=+log%28%28x-1%29%29%2Flog%282%29 ....cross multiply


log%28%283x%2B1%29%29%2Alog%282%29+=+log%28%28x-1%29%29%2Alog%284%29
log%28%283x%2B1%29%29%2Alog%282%29+=+log%28%28x-1%29%29%2Alog%282%5E2%29
log%28%283x%2B1%29%29%2Alog%282%29+=+log%28%28x-1%29%29%2A2log%282%29
log%28%283x%2B1%29%29%2Across%28log%282%29%29+=+log%28%28x-1%29%29%2A2cross%28log%282%29%29
log%28%283x%2B1%29%29+=+2log%28%28x-1%29%29
log%28%283x%2B1%29%29+=+log%28%28x-1%29%5E2%29 ..if log same, then
3x%2B1+=+%28x-1%29%5E2
3x%2B1+=+x%5E2-2x%2B1
0=+x%5E2-2x-3x%2B1-1
0=+x%5E2-5x
x%28x-5%29=0
=>
x=0 ...we can't use this solution because when x approaches zero, log%28b%2Cx%29 goes to -infinity for b+%3E+1 and plus infinity for b+%3C+1, respectively
remember also that you can take the log of a negative number, but your answer is no+longer "real", but complex, means it has an imaginary part to it
or
highlight%28x=5%29 so, this is your solution