Answer:
0.1065
Step-by-step explanation:
Given :[tex]2(3x+1)^5=8[/tex]
Solution :
[tex]2(3x+1)^5=8[/tex]
[tex](3x+1)^5=4[/tex]
Taking natural log both sides
[tex]ln[(3x+1)^5]=ln 4[/tex]
Property : [tex]ln (a^b)=bln(a)[/tex]
[tex]5 ln(3x+1)=ln 4[/tex]
[tex]ln(3x+1)=\frac{1}{5} ln 4[/tex]
[tex]ln(3x+1)=\frac{1}{5} (1.3863)[/tex]
[tex]ln(3x+1)=0.27726[/tex]
[tex]e^{ln(3x+1)}=e^{0.27726}[/tex]
Property : [tex]e^{ln x}=x[/tex]
[tex]3x+1=1.3195[/tex]
[tex]3x=0.3195[/tex]
[tex]x=\frac{0.3195}{3}[/tex]
[tex]x=0.1065[/tex]
Hence the value of x is 0.1065
