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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. \(e^{x} = \dfrac{5}{2}\)

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


    To see the full video page and find related videos, click the following link.
    WIR4 20B M150 V17


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

    \(x=\dfrac{\ln8}{\ln3}\)


    To see the full video page and find related videos, click the following link.
    WIR4 20B M150 V18


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

    No solution.


    To see the full video page and find related videos, click the following link.
    WIR4 20B M150 V19


  4. \(e^{2x} +7 e^{x} - 18 = 0\)

    \(x=\ln 2\)


    To see the full video page and find related videos, click the following link.
    WIR4 20B M150 V20


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

    \(x=\dfrac{125}{4}\)


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    WIR4 20B M150 V21


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

    \(x=0\)


    To see the full video page and find related videos, click the following link.
    WIR4 20B M150 V22


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

    \(x=1\)


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    WIR4 20B M150 V23


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

    \(x=\dfrac{161}{2}\)


    To see the full video page and find related videos, click the following link.
    WIR4 20B M150 V24


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

    No Solution


    To see the full video page and find related videos, click the following link.
    WIR8 20B M150 V11