Chapter 5: Q. 37 (page 315)

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.
$8^{- x} = 1.2$

Short Answer

Expert verified

$x = - \log_{8} 1.2 = \frac{- \ln 1.2}{\ln 8} \approx - 0.088$

Step by step solution

Step 1. Given information

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

$8^{- x} = 1.2$

Step 2. Explanastion

$\begin{array}{l} \Rightarrow 8^{- x} = 1.2 \\ \Rightarrow \log_{8} 8^{- x} = \log_{8} 1.2 \\ \Rightarrow - x = \log_{8} 1.2 \\ \Rightarrow x = - \log_{8} 1.2 \\ \Rightarrow x = - \log_{8} 1.2 = \frac{- \ln 1.2}{\ln 8} \approx - 0.088 \end{array}$

Step 3. Verifying the result

Plot the graph of the equation using the graphing utility as shown below

Hence,

The solution is $x = - 0.088$

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Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.
$8^{- x} = 1.2$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanastion

Step 3. Verifying the result

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Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility. 8-x=1.2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanastion

Step 3. Verifying the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.
$8^{- x} = 1.2$