Question

I need to know how to get x out of the exponent

Answer 1

we have the function

`f(x)=1,822.8(1.4)^x`

when

f(x)=406,500,000,000

Find out the value of x

substitute the given value in the function

`\begin{gathered} 406,500,000,000=1,822.8(1.4)^x \\ (406,500,000,000)/(1,822.8)=1.4^x \end{gathered}`

Apply log on both sides

`\begin{gathered} log(406,500,000,000)/(1,822.8)=log1.4^x \\ \\ log(406,500,000,000)/(1,822.8)=(x)log1.4 \\ \\ x=(log(406,500,000,000)/(1,822.8))/(log1.4) \\ \\ x=57.13 \end{gathered}`

therefore

The answer is x=57