Question

Solve 3x+1 = 15 for x using the change of base formula log, y=

log y
b log b
0-0.594316
O 1.405684
O 1.469743
O 3.469743

Answer 1

Solved given expression for x using the change of base formula log base b of y equals log y over log b is 1.46497

Explanation:

Given Expression:

`3^(x+1)=15`

To solve this, first convert the exponential form into log form

If
`a^(x)=b \text { then } \log _(a) b=x`

So, when comparing the given expression with above, a = 3, x = x + 1 and b = 15.

`3^(x+1)=15` become as
`x+1=\log _(3)(15)`

Now, apply change of base formula to remove base 3 ,

`\log _(a)(y)=(\log y)/(\log a)`

Hence,

`\log _(3)(15)=(\log 15)/(\log 3)`

Substitute
`x+1=\log _(3)(15)` in above expression, we get

`x+1=(\log 15)/(\log 3)`

`x+1=(1.17609)/(0.47712)`

x + 1 = 2.46497

x = 2.46497 - 1

x = 1.46497