Answer
$x=\frac{10^{-.5}-1}{2}\approx-.3419$
Work Step by Step
We are given the equation $\log(2x+1)=-.5$. To solve for x, remember that the base of a common logarithm is understood to be 10.
Therefore, $log(2x+1)=log_{10}2x+1=-.5$.
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $2x+1=10^{-.5}$.
Subtract 1 from both sides.
$2x=10^{-.5}-1$
Divide both sides by 2.
$x=\frac{10^{-.5}-1}{2}\approx-.3419$
