Question

Pls Help, Max Points

Answer 1

`\\ \rm\Rrightarrow 200=5(3)^(x-1)`

`\\ \rm\Rrightarrow 40=3^(x-1)`

`\\ \rm\Rrightarrow ln(4(10))=ln3^(x-1)`

`\\ \rm\Rrightarrow ln4+ln10=(x-1)ln3`

`\\ \rm\Rrightarrow x=(ln4+ln10)/(ln3)+1`

Answer 2

`x=(\ln 40)/(\ln3)+1`

Explanation:

Given equation:

`200=5(3)^(x-1)`

Divide both sides by 5:

`\implies 40=(3)^(x-1)`

Take natural logs of both sides:

`\implies \ln 40=\ln (3)^(x-1)`

`\textsf{Apply the power law}: \quad \ln x^n=n \ln x`

`\implies \ln 40=(x-1)\ln 3`

Divide both sides by ln 3:

`\implies (\ln 40)/(\ln3)=x-1`

Add 1 to both sides:

`\implies x=(\ln 40)/(\ln3)+1`