Chapter 10: Q. 438 (page 1065)

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places
$e^{x} = 23$

Short Answer

Expert verified

The approximate value of x for the equation $e^{x} = 23$ is $3.135$

Step by step solution

Step 1. Given data

The given Logarithmic Equation is $e^{x} = 23$

Step 2. Use logarithms

Take natural logarithms to both sides of the equation

$e^{x} = 23 \ln e^{x} = \ln 23$

Step 3. Apply power property of logarithm

Use power property of logarithm

$\ln e^{x} = \ln 23 x \ln e = \ln 23$

as $\ln (e) = 1$

so $x \ln e = \ln 23 x = \ln 23 x \approx 3.135$

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In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places
$e^{x} = 23$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Use logarithms

Step 3. Apply power property of logarithm

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In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal placesex=23

Short Answer

Step by step solution

Step 1. Given data

Step 2. Use logarithms

Step 3. Apply power property of logarithm

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Pure Maths

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places
$e^{x} = 23$