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Chapter 10: Q. 10.83 (page 1050)

Solve 2ex-2=18. Find the exact answer and then approximate it to three decimal places.

Short Answer

Expert verified

By solving the expression 2ex-2=18, the exact answer of the equation is x=ln9+2and the approximate answer is 4.197

Step by step solution

01

Step 1. Given

An expression2ex-2=18

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.

2ex-2=18ex-2=9ln(ex-2)=ln9

03

Step 3. Use the Power Property

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

lnex-2=ln9x-2=ln9

04

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

Solve the equation. Find the exact answer.

x=ln9+2

The exact answer is x=ln9+2

05

Step 5. Approximate the answer.

x=ln9+2鈮�4.197

The approximate answer is 4.197

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