Question

1. 7 points solve the following equation:

ln(4x + 5)=0

Explanation:

Step1: Recall the property of natural logarithm

If $\ln(a)=b$, then $a = e^{b}$. Here $b = 0$ and $a=4x + 5$, so $4x+5=e^{0}$.

Step2: Evaluate $e^{0}$

Since any non - zero number to the power of 0 is 1, $e^{0}=1$. So the equation becomes $4x + 5=1$.

Step3: Solve for $x$

Subtract 5 from both sides: $4x=1 - 5=-4$. Then divide both sides by 4, $x=\frac{-4}{4}=-1$.

Answer:

$x=-1$