Answer:
[tex]x=\dfrac{\ln 40}{\ln3}+1[/tex]
Step-by-step explanation:
Given equation:
[tex]200=5(3)^{x-1}[/tex]
Divide both sides by 5:
[tex]\implies 40=(3)^{x-1}[/tex]
Take natural logs of both sides:
[tex]\implies \ln 40=\ln (3)^{x-1}[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies \ln 40=(x-1)\ln 3[/tex]
Divide both sides by ln 3:
[tex]\implies \dfrac{\ln 40}{\ln3}=x-1[/tex]
Add 1 to both sides:
[tex]\implies x=\dfrac{\ln 40}{\ln3}+1[/tex]
