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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

[tex]e^x = 6[/tex]
[tex]4^y^+^3 = 3 [/tex]

Respuesta :

We want to solve the two equations
[tex]e^{x}=6[/tex]
and
[tex]4^{y+3}=3[/tex]

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

Second equation.
Take natural log of each side.
[tex]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[/tex]
Answer: y = -2.21 (nearest hundredth)

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