Question

solve the equation.
log _4(2x - 1)=\frac{1}{2}
x = \square (simplify your answer.)

Explanation:

Step1: Convert to exponential form

By the definition of logarithms, if $\log_{a}b = c$, then $b=a^{c}$. So, $\log_{4}(2x - 1)=\frac{1}{2}$ can be rewritten as $2x-1 = 4^{\frac{1}{2}}$.

Step2: Calculate $4^{\frac{1}{2}}$

We know that $4^{\frac{1}{2}}=\sqrt{4}=2$. So the equation becomes $2x - 1=2$.

Step3: Solve for $x$

Add 1 to both sides of the equation: $2x=2 + 1$, so $2x=3$. Then divide both sides by 2, we get $x=\frac{3}{2}$.

Answer:

$\frac{3}{2}$