[tex]$x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex]
Solution:
Given expression:
[tex]$(1.0125)^{4 x}=\frac{3}{2}[/tex]
To solve the expression:
[tex]$(1.0125)^{4 x}=\frac{3}{2}[/tex]
If f(x) = g(x) then ln(f(x)) = ln(g(x)).
Using the above condition, we can write
[tex]$\ln \left(1.0125^{4 x}\right)=\ln \left(\frac{3}{2}\right)[/tex]
Apply log rule: [tex]\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)[/tex]
[tex]$4 x \ln (1.0125)=\ln \left(\frac{3}{2}\right)[/tex]
Divide both side of the equation by [tex]4 \ln (1.0125)[/tex].
[tex]$\frac{4 x \ln (1.0125)}{4 \ln (1.0125)}=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex]
[tex]$x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex]
The answer is [tex]x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex].
