Chapter 10: Q. 10.81 (page 1049)

Solve $7^{x} = 43$ . Find the exact answer and then approximate it to three decimal places.

Short Answer

Expert verified

By solving the expression $7^{x} = 43$ , the exact answer of the equation is $x = \frac{\log 43}{\log 7}$ and the approximate answer is $1.933$

Step by step solution

Step 1. Given

An expression $7^{x} = 43$

To solve the expression.

Step 2. Take the logarithm of both sides

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

$\log 7^{x} = \log 43$

Step 3. Use the Power Property

Use the Power Property to get the $x$ as a factor, not an exponent.

$x \log 7 = \log 43 x = \frac{\log 43}{\log 7}$

The exact answer is $x = \frac{\log 43}{\log 7}$

Step 4. Approximate the answer.

To approximate the answer

x = \frac{\log 43}{\log 7} \approx 1.933

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Solve $7^{x} = 43$ . Find the exact answer and then approximate it to three decimal places.

Short Answer

Step by step solution

Step 1. Given

Step 2. Take the logarithm of both sides

Step 3. Use the Power Property

Step 4. Approximate the answer.

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Solve 7x=43. Find the exact answer and then approximate it to three decimal places.

Short Answer

Step by step solution

Step 1. Given

Step 2. Take the logarithm of both sides

Step 3. Use the Power Property

Step 4. Approximate the answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Mechanics Maths

Calculus

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve $7^{x} = 43$ . Find the exact answer and then approximate it to three decimal places.