Answer: Third Option
[tex]x=1.469743[/tex]
Step-by-step explanation:
We have the following exponential equation
[tex]3^{x+1}=15[/tex]
We must solve the equation for the variable x
To clear the variable x apply the [tex]log_3[/tex] function on both sides of the equation
[tex]log_3(3^{x+1})=log_3(15)[/tex]
Simplifying we get the following:
[tex]x+1=log_3(15)[/tex]
To simplify the expression [tex]log_3 (15)[/tex] we apply the base change property
[tex]log_b(y)=\frac{log(y)}{log(b)}[/tex]
This means that:
[tex]log_3 (15)=\frac{log(15)}{log(3)}[/tex]
Then:
[tex]x+1=\frac{log(15)}{log(3)}[/tex]
[tex]x=\frac{log(15)}{log(3)}-1[/tex]
[tex]x=1.469743[/tex]
