Question

How do you solve `5(1.034)^x-1998=13`?

Answer 1

`x=(ln(402.2))/(ln(1.034))\approx 179.363`

Explanation:

First, rearrange to write it as `5(1.034)^{x}=13+1998=2011`.

Next, divide both sides by `5` to get `1.034^{x}=2011/5=402.2`.

After that, take a logarithm of both sides (it doesn't matter what base you use). I'll use base `e`: `ln(1.034^{x})=ln(402.2)` or, by a property of logarithms, `x*ln(1.034)=ln(402.2)`.

Hence, `x=(ln(402.2))/(ln(1.034))\approx 179.363`.

You should check that this works by substitution back into the original equation.