Question

Erika is working on solving the exponential equation 50^x = 17; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

50^x = 17

Step 02:

exponential equation:

1. Apply logarithms to both sides of the equality.

`log\text{ 50}^x=\text{ log 17}`

2. Apply properties of logarithms.

`x\text{ log 50 = log 17}`

3. Apply the algebraic rules to find the value of x.

`x\text{ = }\frac{log\text{ 17}}{log\text{ 50}}\text{ }`

The answer is:

x = (log 17) / (log 50)