Question

Solve the equation. Check for extraneous solutions. In(7x-4) = In(2x+11)

Answer 1

Question: Solve the equation:

$\ln (7x-4)=\text{ ln(2x+11)}$

Solution:

applying the laws of logarithms (applying the inverse function of the logarithm function) we get:

$e^{\ln (7x-4)}=e^{\text{ ln(2x+11)}}$

this is equivalent to:

$7x-4=\text{ 2x+11}$

putting similar terms together we get:

$7x-2x=11+4$

this is equivalent to:

$5x\text{ = 15}$

solving for x, we get:

$x\text{ = }\frac{15}{5}\text{ = 3}$

then, we can conclude that the solution of the equation is:

$x\text{ = 3}$