Exponential to Logarithmic

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions can be expressed in terms of logarithmic functions, and vice versa. If a^b = c, then log_a(c) = b.

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, log_b(a) = c means b^c = a.

Front

What is the base of a logarithm?

Back

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

Front

How do you convert an exponential equation to a logarithmic equation?

Back

To convert an exponential equation a^b = c to logarithmic form, write it as log_a(c) = b.

Front

What is the logarithmic form of the equation 3^2 = 9?

Back

The logarithmic form is log_3(9) = 2.

Front

What is the logarithmic form of the equation 5^3 = 125?

Back

The logarithmic form is log_5(125) = 3.

Front

If x^y = z, how can you express y in terms of logarithms?

Back

You can express y as y = log_x(z).

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_a(b) = log_c(b) / log_c(a) for any positive c.

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.