Exponential and Log Forms

Front

What is the exponential form of \( \log_{6}t=m \)?

Back

\( 6^{m}=t \)

Front

Evaluate \( \log_{5}\sqrt{5} \)

Back

\( \frac{1}{2} \) or 0.5

Front

Change to Exponential Form: \( \log_{6}36 = 2 \)

Back

\( 6^{2}=36 \)

Front

Evaluate \( \log_{8}64 \)

Back

2

Front

Rewrite in exponential form: \( \log_{4}\frac{1}{64}=-3 \)

Back

\( 4^{-3} = \frac{1}{64} \)

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

If \( \log_{b}a = c \), what is the equivalent exponential form?

Back

\( b^{c} = a \)

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is \( e \) (approximately 2.718).

Front

Evaluate \( \log_{10}1000 \)

Back

3

Front

What is the change of base formula for logarithms?

Back

\( \log_{b}a = \frac{\log_{k}a}{\log_{k}b} \) for any base \( k \).