How do you solve log(5-2x)=log(3x +1)?

1 Answer
Aug 9, 2015

$\textcolor{red}{x = \frac{4}{5}}$

Explanation:

log(5−2x)=log(3x+1)

Convert the logarithmic equation to an exponential equation.

${10}^{\log \left(5 - 2 x\right)} = {10}^{\log \left(3 x + 1\right)}$

Remember that ${10}^{\log} x = x$, so

$5 - 2 x = 3 x + 1$

$4 = 5 x$

$x = \frac{4}{5}$

Check:

log(5−2x)=log(3x+1)

If $x = \frac{4}{5}$,

log(5−2(4/5))=log(3(4/5)+1)

$\log \left(5 - \frac{8}{5}\right) = \log \left(\frac{12}{5} + 1\right)$

$\log \left(\frac{25 - 8}{5}\right) = \log \left(\frac{12 + 5}{5}\right)$

$\log \left(\frac{17}{5}\right) = \log \left(\frac{17}{5}\right)$

$x = \frac{4}{5}$ is a solution.