# Section 3.4 – Exponential and Logarithmic Equations

Section Details.
• Solving exponential equations and being careful not to take a logarithm of a negative number
• Solving logarithmic equations and checking for extraneous solutions

### Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.
Solve each of the following for $$x$$. Always check for extraneous solutions.
1. $$e^{x} = \dfrac{5}{2}$$

$$x=\ln\left(\dfrac{5}{2}\right)$$

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2. $$3^{x} + 7 = 15$$, using the common logarithm

$$x=\dfrac{\ln8}{\ln3}$$

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3. $$\dfrac{15}{100 + e^{2x}} = 3$$

No solution.

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4. $$e^{2x} +7 e^{x} - 18 = 0$$

$$x=\ln 2$$

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5. $$\log_5(4y) = 3$$

$$x=\dfrac{125}{4}$$

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6. $$\log_5 (x+2) + \log_5 (x+3) = \log_5 (6)$$

$$x=0$$

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7. $$\log_5 (x) + \log_5 (x + 4) = 1$$

$$x=1$$

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8. $$\log_3 (x+2) - \log_3 (2x ) = 4$$

$$x=\dfrac{161}{2}$$

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9. $$\log_6(x-12)-\log_6(x)=\log_6(x-6)$$

No Solution

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