Logs: Conversions to Exponentials and Vice Versa

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 5^2 = 25 to logarithmic form.

Back

log_5(25) = 2.

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

Rewrite the logarithmic equation log_10(100) = 2 in exponential form.

Back

10^2 = 100.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

Convert the logarithmic equation log_2(16) = 4 to exponential form.

Back

2^4 = 16.

Front

What does it mean if log_b(a) = c?

Back

It means that b raised to the power of c equals a.

Front

Rewrite the equation y = 3^x in logarithmic form.

Back

log_3(y) = x.

Front

What is the definition of the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.718.

Front

Convert the equation 7 = 2^x to logarithmic form.

Back

log_2(7) = x.