question solve for the exact value of x. 2 ln(7x + 6) - 2 = 12

Explanation:

Step1: Isolate the logarithmic term

Add 2 to both sides of the equation: $2\ln(7x + 6)-2 + 2=12 + 2$ $2\ln(7x + 6)=14$

Step2: Solve for the natural - logarithm term

Divide both sides by 2: $\frac{2\ln(7x + 6)}{2}=\frac{14}{2}$ $\ln(7x + 6)=7$

Step3: Convert from logarithmic to exponential form

Since $\ln a=b$ is equivalent to $e^{b}=a$, we have: $e^{7}=7x + 6$

Step4: Isolate x

Subtract 6 from both sides: $e^{7}-6=7x$ Then divide both sides by 7: $x=\frac{e^{7}-6}{7}$

Answer:

$x=\frac{e^{7}-6}{7}$