Question

what is the value of x in this equation? ln(x + 4) - ln(2x - 1) = 0 options: -3, -4, 4, 5

Explanation:

Step1: Rearrange the logarithmic equation

$\ln(x+4) = \ln(2x-1)$

Step2: Cancel natural logs (one-to-one property)

$x+4 = 2x-1$

Step3: Solve for $x$

$4 + 1 = 2x - x$
$x = 5$

Step4: Verify domain validity

For $\ln(x+4)$: $5+4=9>0$; for $\ln(2x-1)$: $2*5-1=9>0$. Both are valid.

Answer:

$\boldsymbol{5}$ (Option: $\boldsymbol{\bigcirc 5}$)