Properties of Logarithms & Exponents

Help Questions

Algebra › Properties of Logarithms & Exponents

Questions 1 - 5

1

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$

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

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

2

Convert the expression from logarithmic to exponential.

$\log_6 216=3$

$216=6^{1/3}$

$216=3^{1/6}$

$216^{1/6}=3$

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

3

Convert the expression from logarithmic to exponential.

$\log_3 9=2$

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

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

4

Convert the expression from logarithmic to exponential.

$\log_4 1024=5$

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

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

5

Convert the expression from logarithmic to exponential.

$\log_6 216=3$

$216=6^{1/3}$

$216=3^{1/6}$

$216^{1/6}=3$

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

Return to subject