Solving an exponential equation

To solve an exponential equation, take the log of both sides, and solve for the variable.

Step-by-step explanation:

Example 1: Solve for x in the equation tex2html_wrap_inline119.

Solution:

Step 1: Take the natural log of both sides:

displaymath121

Step 2: Simplify the left side of the above equation using Logarithmic Rule 3:

displaymath123

Step 3: Simplify the left side of the above equation: Since Ln (e) = 1, the equation reads

displaymath127

Ln (80) is the exact answer and x=4.38202663467 is an approximate answer because we have rounded the value of Ln (80) ...

Check: Check your answer in the original equation.

displaymath131