# How do you solve 20=50(1.04)^x?

Dec 21, 2015

-23.36241894

The answer can be rounded up according to the requirements

#### Explanation:

$20 = 50 {\left(1.04\right)}^{x}$

Step 1: Isolate the term containing the exponent to one side of the equation. This is achieved by dividing both sides by 50.

$\frac{20}{50} = {\left(1.04\right)}^{x}$
$0.4 = {\left(1.04\right)}^{x}$

Step 2: in order to solve for "x" we have to use the power rule of logarithms i.e. $\log \left({A}^{n}\right) = n \log \left(A\right)$ note you can use ln( ) or log( ) depending on your choice.

Let us take log to the base 10.

$\log \left(0.4\right) = \log {\left(1.04\right)}^{x}$
$\log \left(0.4\right) = x \log \left(1.04\right)$

Step 3: Divide both sides by log (1.04).
$\log \frac{0.4}{\log} \left(1.04\right) = x$

$x = - 23.36241894$