Question

solve the equation below for x. log2x+log(2x-1)=log3x

a. x=0,5/4
b. x=5/2
c. x=5/4
d. There are no solutions

Answer 1

rewrite using properties of logs...
\[\log 2x + \log \left( 2x-1 \right) = \log 2x \left( 2x-1 \right)= \log \left( 4x ^{2}-2x \right)=\log 3x \]
\[ \rightarrow \log \left( 4x ^{2}-2x \right)-\log 3x = 0\rightarrow \log \left( \frac{4x ^{2}-2x}{3x} \right) = 0\rightarrow \log \left( \frac{4x -2}{3} \right) = 0\]
so (4x-2)/3 = 1 solve for x