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Chapter 11: Q61. (page 582)

Solve each equation.
$3 e^{x} - 2 = 0$

Short Answer

Expert verified

The solution to the equation is $\ln (\frac{2}{3})$ .

Step by step solution

01

Step 1. Given Information.

Given equation is $3 e^{x} - 2 = 0$

02

Step 2. Calculation.

Simplifying the equation:

$\begin{array}{l} 3 e^{x} - 2 = 0 \\ 3 e^{x} = 2 \\ e^{x} = \frac{2}{3} \\ \ln (e^{x}) = \ln (\frac{2}{3}) \\ x = \ln (\frac{2}{3}) \end{array}$

03

Step 3. Conclusion.

Hence, the solution to the equation is $x = \ln (\frac{2}{3})$ .

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Most popular questions from this chapter

Find the first five terms of each arithmetic sequence described.

$a_{1} = \frac{4}{3}, d = - \frac{1}{3}$

Find $a_{8}$ if $a_{n} = 4 + 3 n$

Find the first five terms of each arithmetic sequence described.

$a_{1} = 5, d = 3$

Find $S_{n}$ for each arithmetic series described.

$a_{1} = 4, a_{n} = 100, n = 25$

The African-American festival of Kwanzaa includes a ritual involving candles. The first night, a candle is lit and then blown out. The second night, a new candle and the candle from the previous night are lit and blown out. This pattern of lighting a new candle and relighting all the candles from the previous nights is continued for seven nights.Use a formula from this lesson to find the total number of candle lightings during the festival.

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