SOLUTION: Log4(x-1)+log4(3x-1)=2

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Question 826553: Log4(x-1)+log4(3x-1)=2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


log%284%2C%28x-1%29%29%2Blog%284%2C%283x-1%29%29=2
log%284%2C%28%28x-1%29%283x-1%29%29%29=2..............convert into log base 10
log%28%28x-1%29%283x-1%29%29%2Flog%284%29=2
log%28%28x-1%29%283x-1%29%29=2log%284%29

%28x-1%29%283x-1%29=16..............solve for x

3x%5E2-x-3x%2B1=16
3x%5E2-4x%2B1-16=0
3x%5E2-4x-15=0............factor completely, first replace -4x with -9x%2B5x
3x%5E2-9x%2B5x-15=0..............group
%283x%5E2-9x%29%2B%285x-15%29=0....factor out 3x from the first term and 5 from the second term
3x%28x-3%29%2B5%28x-3%29=0
%28x-3%29%283x%2B5%29+=+0
solutions:
if+x-3=0 => x=3
if 3x%2B5=0 => x=-5%2F3
since we have log, consider only x=3 as a solution