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High School Math : Solving Logarithmic Equations

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Example Questions

Example Question #1 : Solving And Graphing Logarithmic Equations

Solve the equation.

$3^{3x-7}=81^{12-3x}$

Possible Answers:

$x=\frac{11}{3}$

x=9

x=33

$x=\frac{22}{3}$

x=11

Correct answer:

$x=\frac{11}{3}$

Explanation:

Change 81 to 3^4 so that both sides have the same base. Once you have the same base, apply log to both sides so that you can set the exponential expressions equal to each other ( 3x-7 = 48-12x ). Thus, $x=\frac{11}{3}$ .

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Example Question #2 : Solving And Graphing Logarithmic Equations

Solve the equation.

$36^{10x+2}=(\frac{1}{6})^{13-x}$

Possible Answers:

x=17

x=19

$x=\frac{11}{19}$

$x=-\frac{17}{19}$

$x=\frac{17}{19}$

Correct answer:

$x=-\frac{17}{19}$

Explanation:

Change the left side to 6^2 and the right side to $6^{-1}$ so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other ( 20x+4=-13+x ). $x=-\frac{17}{19}$ .

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Example Question #3 : Solving And Graphing Logarithmic Equations

Solve the equation.

$8^{x-1}=(\frac{1}{16})^{4x-3}$

Possible Answers:

$x=\frac{11}{19}$

x=13

x=30

$x=\frac{15}{19}$

x=15

Correct answer:

$x=\frac{15}{19}$

Explanation:

Change the left side to 2^3 and the right side to $2^{-4}$ so that both sides have the same base. Apply log and then set the exponential expressions equal to each other ( 3x-3=-16x+12 ). Thus, $x=\frac{15}{19}$ .

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Example Question #4 : Solving And Graphing Logarithmic Equations

Solve the equation.

$25^{20x+4}=(\frac{1}{125})^{4-3x}$

Possible Answers:

$x=-\frac{20}{31}$

x=18

$x=-\frac{11}{31}$

$x=\frac{9}{40}$

$x=\frac{20}{31}$

Correct answer:

$x=-\frac{20}{31}$

Explanation:

Change the left side to 5^2 and the right side to $5^{-3}$ so that both sides have the same base. Apply log and then set the exponential expressions equal to each other ( 40x+8=-12+9x ). Thus, $x=-\frac{20}{31}$

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Example Question #5 : Solving And Graphing Logarithmic Equations

Solve the equation.

$27^{4x-1}=(\frac{1}{3})^{3x+8}$

Possible Answers:

x=1

x=3

$x=\frac{1}{3}$

$x=-\frac{1}{3}$

x=-1

Correct answer:

$x=-\frac{1}{3}$

Explanation:

Change the left side to 3^3 and the right side to $3^{-1}$ so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other ( 12x-3=-3x-8 ). Thus, $x=-\frac{1}{3}$ .

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Example Question #6 : Solving And Graphing Logarithmic Equations

Solve for .

$17 + x = \log_{10}10000$

Possible Answers:

983

10^1^7

10^4 - 17

Correct answer:

Explanation:

$log_{10}10000$ can be simplified to since 10^4 = 10000 . This gives the equation:

17 + x = 4

Subtracting from both sides of the equation gives the value for .

$(17 + x) - 17 = (4) - 17 \rightarrow x = -13$

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Example Question #7 : Solving And Graphing Logarithmic Equations

Solve the equation.

$5^{3x-9}=25^{^{x+5}$

Possible Answers:

x=19

x=5

x=21

x=10

x=11

Correct answer:

x=19

Explanation:

First, change 25 to 5^2 so that both sides have the same base. Once they have the same base, you can apply log to both sides so that you can set their exponents equal to each other, which yields 3x-9=2x+10 .

x=19

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Example Question #8 : Solving And Graphing Logarithmic Equations

Solve the equation.

$7^{3x+4}=49^{x+1}$

Possible Answers:

x=4

x=-2

x=-1

x=2

x=-4

Correct answer:

x=-2

Explanation:

Change 49 to 7^2 so that both sides have the same base so that you can apply log. Then, you can set the exponential expressions equal to each other 3x+4=2x+2 .

Thus, x=-2

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Example Question #1 : Solving Logarithmic Equations

Solve the equation.

$10^{2x-10}=(\frac{1}{100})^{8x-1}$

Possible Answers:

$x=\frac{2}{3}$

$x=\frac{1}{3}$

x=-1

$x=-\frac{2}{3}$

x=1

Correct answer:

$x=\frac{2}{3}$

Explanation:

Change the right side to $10^{-2}$ so that both sides have the same bsae of 10. Apply log and then set the exponential expressions equal to each other

2x-10=-16x+2

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Example Question #10 : Solving And Graphing Logarithmic Equations

Solve the equation.

$4^{2x-7}=64^{3x}$

Possible Answers:

x=1

x=8

x=7

x=-1

x=10

Correct answer:

x=-1

Explanation:

Change 64 to 4^3 so that both sides have the same base. Apply log to both sides so that you can set the exponential expressions equal to each other

2x-7=9x .

Thus, x=-1 .

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All High School Math Resources

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High School Math : Solving Logarithmic Equations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Solving And Graphing Logarithmic Equations

Example Question #2 : Solving And Graphing Logarithmic Equations

Example Question #3 : Solving And Graphing Logarithmic Equations

Example Question #4 : Solving And Graphing Logarithmic Equations

Example Question #5 : Solving And Graphing Logarithmic Equations

Example Question #6 : Solving And Graphing Logarithmic Equations

Example Question #7 : Solving And Graphing Logarithmic Equations

Example Question #8 : Solving And Graphing Logarithmic Equations

Example Question #1 : Solving Logarithmic Equations

Example Question #10 : Solving And Graphing Logarithmic Equations

All High School Math Resources

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