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Flashcards: Properties of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_6 216=3$ $\displaystyle \log_6 216=3$

6^3=216 $\displaystyle 6^3=216$

3^6=216 $\displaystyle 3^6=216$

$216=3^{1/6}$ $\displaystyle 216=3^{1/6}$

$216^{1/6}=3$ $\displaystyle 216^{1/6}=3$

$216=6^{1/3}$ $\displaystyle 216=6^{1/3}$

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Flashcards: Properties of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_6 216=3$ $\displaystyle \log_6 216=3$

6^3=216 $\displaystyle 6^3=216$

3^6=216 $\displaystyle 3^6=216$

$216=3^{1/6}$ $\displaystyle 216=3^{1/6}$

$216^{1/6}=3$ $\displaystyle 216^{1/6}=3$

$216=6^{1/3}$ $\displaystyle 216=6^{1/3}$

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Flashcards: Properties of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_6 216=3$ $\displaystyle \log_6 216=3$

Your answer:

3^6=216 $\displaystyle 3^6=216$

Your answer:

$216=3^{1/6}$ $\displaystyle 216=3^{1/6}$

Your answer:

$216^{1/6}=3$ $\displaystyle 216^{1/6}=3$

Your answer:

$216=6^{1/3}$ $\displaystyle 216=6^{1/3}$

Correct answer:

6^3=216 $\displaystyle 6^3=216$

Explanation:

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

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

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

$\log_6 216=3$ $\displaystyle \log_6 216=3$

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

The exponential form becomes

6^3=216 $\displaystyle 6^3=216$

Flashcards: Properties of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$ $\displaystyle \log_4 1024=5$

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

$\displaystyle 5^4=1020$

$\displaystyle 4^5=1025$

$\displaystyle 5^4=1024$

$\displaystyle 4^5=1024$

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Flashcards: Properties of Logarithms & Exponents

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$ $\displaystyle \log_4 1024=5$

Your answer:

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

Your answer:

$\displaystyle 5^4=1020$

Your answer:

$\displaystyle 4^5=1025$

Your answer:

$\displaystyle 5^4=1024$

Correct answer:

$\displaystyle 4^5=1024$

Explanation:

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

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

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

$\log_4 1024=5$ $\displaystyle \log_4 1024=5$

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

The exponential form becomes

$\displaystyle 4^5=1024$

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