Question

solve for x. \\(\log_{5}(2x - 4) = 2\\) \\(x = \square\\)

Explanation:

Step1: Convert logarithmic to exponential form

Recall that if $\log_{a}b = c$, then $a^{c}=b$. For $\log_{5}(2x - 4)=2$, we have $5^{2}=2x - 4$.

Step2: Calculate $5^{2}$ and solve for x

We know that $5^{2}=25$, so the equation becomes $25 = 2x - 4$. Add 4 to both sides: $25 + 4=2x$, which simplifies to $29 = 2x$. Then divide both sides by 2: $x=\frac{29}{2}=14.5$.

Answer:

$\frac{29}{2}$ (or 14.5)