Question

Solve 3^x+1 = 15 for x using the change of base formula log base b of y equals log y over log b

Answer 1

Answer:

x= 1.46497

Step-by-step explanation:

$3^{x+1} = 15$

To solve this , first we convert the exponential form in to log form

$if \ a^x=b \ then \ log_a(b)=x$

$3^{x+1} = 15$ becomes $log_3(15)= x+1$

now we apply change of base formula to remove base 3

$log_b(y)= \frac{log y}{log b}$

like that log_3(15) becomes

$log_3(15)= \frac{log 15}{log 3}$

$\frac{log 15}{log 3}= x+1$

2.46497=x+1

subtract 1 from both sides

x= 1.46497

Answer 2

Answer:

The value of x is 1.46.

Step-by-step explanation:

Given : Equation $3^{x+1}=15$

To find : Solve for x using the change of base formula log base b of y equals log y over log b ?

Solution :

Equation $3^{x+1}=15$

Applying the logarithmic property,

$a^x=b\Rightarrow \log_a(b)=x$

$3^{x+1}=15\Rightarrow \log_3(15)=x+1$

Applying change base formula in LHS,

$log_b(y)= \frac{log y}{log b}$

$\frac{log 15}{log 3}=x+1$

$2.46=x+1$

$x=2.46-1$

$x=1.46$

Therefore, the value of x is 1.46.