Converting Between Exponential and Logarithmic Form

Front

What is the definition of logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, in the expression \(\log_b(a) = c\), \(b^c = a\).

Front

What is the relationship between exponential and logarithmic forms?

Back

Exponential form \(b^c = a\) can be rewritten in logarithmic form as \(\log_b(a) = c\).

Front

Convert \(\log_5(125) = 3\) to exponential form.

Back

The exponential form is \(5^3 = 125\).

Front

Convert \(8^x = 64\) to logarithmic form.

Back

The logarithmic form is \(\log_8(64) = x\).

Front

What is the base in the logarithmic expression \(\log_b(a)\)?

Back

The base \(b\) is the number that is raised to a power to obtain \(a\).

Front

How do you convert \(\log_7(50) = x\) to exponential form?

Back

The exponential form is \(7^x = 50\).

Front

What is the value of \(\log_2(8)\)?

Back

The value is 3, because \(2^3 = 8\).

Front

If \(b^c = a\), what is \(\log_b(a)\)?

Back

\(\log_b(a) = c\).

Front

Convert \(3 = 7^x\) to logarithmic form.

Back

The logarithmic form is \(\log_7(3) = x\).

Front

What is the definition of exponential form?

Back

Exponential form expresses a number as a base raised to a power, such as \(b^c = a\).