Chapter 5: Q 99. (page 299)

Solve the equation.
$e^{3 x} = 10$

Short Answer

Expert verified

The solution to the equation, $e^{3 x} = 10$ is, $x = \frac{1}{3} \ln 10$ .

Step by step solution

Step 1. Given Information

The given equation to be solved is $e^{3 x} = 10$ .

Step 2. Formula used

Rule of change from logarithm to exponents:

$\log_{a} b = y \Rightarrow a^{y} = b$

Step 3. Finding Solution

The given equation is $e^{3 x} = 10$ .

Take logarithm on both sides.

$\ln e^{3 x} = \ln 10 3 x \ln e = \ln 10 3 x = \ln 10 x = \frac{1}{3} \ln 10$

The solution to the given equationis, $x = \frac{1}{3} \ln 10$ .

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Solve the equation.
$e^{3 x} = 10$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Formula used

Step 3. Finding Solution

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Solve the equation.e3x=10

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Formula used

Step 3. Finding Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the equation.
$e^{3 x} = 10$