Answer:
x=0.83
Step-by-step explanation:
Given: [tex]e^{3x}=12[/tex]
We are given an exponential equation and to solve for x.
[tex]e^{3x}=12[/tex]
Taking ln both sides
[tex]\ln e^{3x}=\ln 12[/tex]
[tex]3x\ln e=\ln 12[/tex] [tex]\because ln a^m=m\ln a[/tex]
[tex]3x=\ln 12[/tex] [tex]\because \ln e=1[/tex]
[tex]x=\dfrac{\ln 12}{3}[/tex] [tex]\text{divides both sides by 3}[/tex]
The exact value of x is [tex]\dfrac{\ln 12}{3}[/tex]
Using calculator to find ln 12
[tex]x=\dfrac{2.4849}{3}[/tex]
[tex]x=0.8283[/tex]
Hence, The value of x is 0.83
