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Algebra 3/4 : Properties of Logarithms & Exponents

Study concepts, example questions & explanations for Algebra 3/4

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6 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_6 216=3$

Possible Answers:

$216=3^{1/6}$

6^3=216

$216^{1/6}=3$

3^6=216

$216=6^{1/3}$

Correct answer:

6^3=216

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_6 216=3$

$\\b=6 \\a=216 \\c=3$

The exponential form becomes

6^3=216

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Example Question #2 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$

Possible Answers:

5^4=1020

5^4=1024

$1024^\frac{1}{4}=5$

4^5=1024

4^5=1025

Correct answer:

4^5=1024

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_4 1024=5$

$\\b=4 \\a=1024 \\c=5$

The exponential form becomes

4^5=1024

Report an Error

Example Question #3 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_3 9=2$

Possible Answers:

3^2=9

3^3=9

9^2=3

$9^\frac{1}{3}=2$

2^3=9

Correct answer:

3^2=9

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_3 9=2$

$\\b=3 \\a=9 \\c=2$

The exponential form becomes

3^2=9

Report an Error

Example Question #4 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_6 216=3$

Possible Answers:

$216^{1/6}=3$

$216=3^{1/6}$

$216=6^{1/3}$

6^3=216

3^6=216

Correct answer:

6^3=216

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_6 216=3$

$\\b=6 \\a=216 \\c=3$

The exponential form becomes

6^3=216

Report an Error

Example Question #5 : Properties Of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$

Possible Answers:

5^4=1020

4^5=1024

$1024^\frac{1}{4}=5$

5^4=1024

4^5=1025

Correct answer:

4^5=1024

Explanation:

To convert the logarithmic expression to exponential form, recall the change of base formula.

$\log_b a=c\rightarrow b^c=a$

Apply the change of base formula to this particular logarithmic expression.

$\log_4 1024=5$

$\\b=4 \\a=1024 \\c=5$

The exponential form becomes

4^5=1024

Report an Error

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Algebra 3/4 : Properties of Logarithms & Exponents

Study concepts, example questions & explanations for Algebra 3/4

All Algebra 3/4 Resources

Example Questions

Example Question #1 : Properties Of Logarithms & Exponents

Example Question #2 : Properties Of Logarithms & Exponents

Example Question #3 : Properties Of Logarithms & Exponents

Example Question #4 : Properties Of Logarithms & Exponents

Example Question #5 : Properties Of Logarithms & Exponents

All Algebra 3/4 Resources

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