Question

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

Solve for the variable in the equations below.
Round your answers to the nearest hundredth.
Do not round any intermediate computations.

e^x = 6

4^(y+3) = 3


`e^x = 6`

`4^y^+^3 = 3`

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= (ln(3))/(ln(4)) =0.7925\\y=0.7925-3=-2.2075`
Answer: y = -2.21 (nearest hundredth)