Question

Solve for n: 400(1.16)^n=35,120

Answer 1

The given equation is:

`400\left(1.16\right)^n=35120`

It is required to solve the equation for the value of n.

Divide both sides of the equation by 400:

`\begin{gathered} (400\left(1.16\right)^n)/(400)=(35120)/(400) \\ \\ \Rightarrow\left(1.16\right)^n=(439)/(5) \end{gathered}`

Take the logarithm of both sides of the equation:

`\begin{gathered} \log(1.16)^n=\log\left((439)/(5)\right) \\ \text{ Apply the power property of logarithms:} \\ \Rightarrow n\log(1.16)=\log\left((439)/(5)\right) \end{gathered}`

Divide both sides by log (1.16):

The value of n is about 30.151.