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Chapter 10: Q. 10.84 (page 1050)

Solve 5e2x=25. Find the exact answer and then approximate it to three decimal places.

Short Answer

Expert verified

By solving the expression 5e2x=25, the exact answer of the equation is x=ln52and the approximate answer is 0.805

Step by step solution

01

Step 1. Given

An expression5e2x=25

To solve the expression.

02

Step 2. Take the natural logarithm of both sides

Since the exponential is isolated, take the natural logarithm of both sides.

e2x=5lne2x=ln5

03

Step 3. Use the Power Property

Use the Power Property to get the xas a factor, not an exponent.

2x(lne)=ln52x=ln5

04

Step 4. Solve the equation. Find the exact answer.

Solve the equation. Find the exact answer.

2x=ln5x=ln52

The exact answer is x=ln52

05

Step 5. Approximate the answer.

x=ln52鈮�0.805

The approximate answer is 0.805

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