Question

I don't understand this and would appreciate an explanation as well :)

Answer 1

We want to solve the two equations
$e^{x}=6$
and
$4^{y+3}=3$

First equation.
Take natural log of each side.
$ln(e^{x})=ln(6)\\xln(e)=ln(6)\\ x=ln(6)=1.7918$
Note that ln(e) = 1 by definition.
Answer: x = 1.79 (nearest hundredth)

Second equation.
Take natural log of each side.
$ln(4^{y+3})=ln(3)\\ (y+3)ln(4)=ln(3)\\ y+3= \frac{ln(3)}{ln(4)} =0.7925\\y=0.7925-3=-2.2075$
Answer: y = -2.21 (nearest hundredth)