Converting Logarithms and Exponentials

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. For example, in the equation log_b(a) = c, b^c = a.

Front

Convert the exponential equation 2^3 = 8 into logarithmic form.

Back

log_2(8) = 3

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

Rewrite the equation 10^2 = 100 in logarithmic form.

Back

log_10(100) = 2

Front

Evaluate log_3(27).

Back

3

Front

Convert the logarithmic equation log_4(16) = x into exponential form.

Back

4^x = 16

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a certain value. In log_b(a), b is the base.

Front

If log_5(25) = x, what is the value of x?

Back

2

Front

Convert the equation log_2(8) = 3 into exponential form.

Back

2^3 = 8

Front

What does it mean to evaluate a logarithm?

Back

To evaluate a logarithm means to find the exponent that the base must be raised to in order to equal a given number.