Option D:
x = 2.06
Solution:
Given equation is [tex]2^{3x}=73[/tex].
To find the value of x:
If f(x) = g(x), then [tex]\ln (f(x))=\ln (g(x))[/tex].
Raise ln on both sides of the equation.
[tex]\ln 2^{3x}=\ln73[/tex]
Using log rule: [tex]\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)[/tex]
[tex]3 x \ln (2)=\ln 73[/tex]
Divide by 3ln(2) on both sides.
[tex]$\frac{3 x \ln (2)}{3 \ln (2)}=\frac{\ln (73)}{3 \ln (2)}[/tex]
[tex]$x=\frac{\ln (73)}{3 \ln (2)}[/tex]
x = 2.0632
x = 2.06
Hence Option D is the correct answer.
