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Chapter 10: Q. 309 (page 1054)

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal
places.

4x=112

Short Answer

Expert verified

The exact solution of the exponential equation 4x=112is x=log(112)log(4)and the approximate solution is 3.404which is rounded to three decimal places.

Step by step solution

01

Step 1. Given

An exponential equation4x=112

To solve the exponential equation

02

Step 2. Take logarithm on both sides

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

log(4x)=log(112)

03

Step 3. Use the Power Property

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

xlog(4)=log(112)

04

Step 4. Solve for x 

Solve for xand find the exact answer.

xlog(4)=log(112)x=log(112)log(4)

05

Step 5. Approximate the answer

x=log(112)log(4)=3.404

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