Question

solve for x. \\(\ln 16 = \ln(2x + 1)\\) \\(x = \square\\)

Explanation:

Step1: Use the property of logarithms

If $\ln a = \ln b$, then $a = b$ (for the natural logarithm, the argument must be positive, and here both $\ln 16$ and $\ln(2x + 1)$ are defined when $2x+1>0$ and $16>0$ which is true, so we can set the arguments equal). So we have $16 = 2x + 1$.

Step2: Solve for x

Subtract 1 from both sides: $16 - 1 = 2x + 1 - 1$, which simplifies to $15 = 2x$. Then divide both sides by 2: $x=\frac{15}{2}=7.5$.

Answer:

$7.5$ (or $\frac{15}{2}$)