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Chapter 10: Q. 10.82 (page 1050)

Solve 8x=98. Find the exact answer and then approximate it to three decimal places.

Short Answer

Expert verified

By solving the expression 8x=98, the exact answer of the equation is x=log98log8and the approximate answer is 2.205

Step by step solution

01

Step 1. Given

An expression8x=98

To solve the expression.

02

Step 2. Take the logarithm of both sides

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

log8x=log98

03

Step 3. Use the Power Property

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

xlog8=log98x=log98log8

The exact answer is x=log98log8

04

Step 4. Approximate the answer.

x=log98log8鈮�2.205

The approximate answer is 2.205

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