Question 1078094: How do you expand log10 x+log10(3x-5)=log10^2? I tried to solve this equation but I can't figure it out.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! log10 x+log10(3x-5)=log10 2
adding logs is multiplication of what the log is of.
x(3x-5)=2, by raising everything to the 10 power.
3x^2-5x-2=0
(3x+1)(x-2)=0
x=-1/3, 2. Logs can't be negative, so x=2
check
log10 2+ log10(1)=log10 2
log10 (1)=0
log10 2=1og 10 2
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