Respuesta :

Change of the base rule of logarithm function is used to convert the base of the logarithm to the base of 10 or e form. The value x for the given function is 1.469743. Hence the option 3 is the correct option.

Given information-

The given function in the problem is,

[tex]3^{x+1}=15[/tex]

Change of the base rule

Change of the base rule of logarithm function is used to convert the base of the logarithm to the base of 10 or e form.

Suppose y and b are the positive real numbers and e is the exponential number. Then by the change of the base rule we can write,

[tex]\log_b y=\dfrac{\log_e y}{\log_e b}[/tex]

[tex]\log_b y=\dfrac{\log y}{\log b}[/tex]

The given function is,

[tex]3^{x+1}=15[/tex]

Let logarithm function both side,

[tex]\log3^{x+1}=\log15[/tex]

[tex](x+1)\log3=\log15[/tex]

Divide by the [tex]\log 3[/tex] both the sides

[tex](x+1)=\dfrac{\log15}{\log3}[/tex]

[tex](x+1)=\log_315[/tex]

[tex](x+1)=2.465[/tex]

Subtract with 1 both the sides,

[tex]x=2.469743-1[/tex]

[tex]x=1.469743[/tex]

Thus the value x for the given function is 1.469743. Hence the option 3 is the correct option.

Learn more about the Change of the base rule here;

https://brainly.com/question/13501523

Otras preguntas