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Chapter 10: Q. 308 (page 1054)

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

5x=110

Short Answer

Expert verified

The exact solution of the exponential equation 5x=110is x=log(110)log(5)and the approximate solution is 2.921which is rounded to three decimal places.

Step by step solution

01

Step 1. Given

An exponential equation5x=110

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(5x)=110

03

Step 3. Use the Power Property

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

xlog(5)=log(110)

04

Step 4. Solve for x 

Solve for xand find the exact answer.

xlog(5)=log(110)x=log(110)log(5)
05

Step 5. Approximate the answer

x=log(110)log(5)=2.921

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