Question

$5 in a $10 general admission Night o f the Free with Sultos 10 show that Moderneature.com 1 3114111 ALLSTON NATIONAL THEATRE 9. Solve for x: (Round answer to two decimal points.) 2(3x + 1) = 8 2(3x+1)^5 = 8

Answer 1

0.1065

Explanation:

Given :
`2(3x+1)^5=8`

Solution :

`2(3x+1)^5=8`

`(3x+1)^5=4`

Taking natural log both sides

`ln[(3x+1)^5]=ln 4`

Property :
`ln (a^b)=bln(a)`

`5 ln(3x+1)=ln 4`

`ln(3x+1)=(1)/(5) ln 4`

`ln(3x+1)=(1)/(5) (1.3863)`

`ln(3x+1)=0.27726`

`e^(ln(3x+1))=e^(0.27726)`

Property :
`e^(ln x)=x`

`3x+1=1.3195`

`3x=0.3195`

`x=(0.3195)/(3)`

`x=0.1065`

Hence the value of x is 0.1065