M3 converting logs and exponentials

Front

Rewrite as a log: 7^0 = 1

Back

log_7(1) = 0

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

Convert the exponential equation 10^x = 100 to logarithmic form.

Back

log_10(100) = x

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.

Front

If log_b(a) = c, what is the equivalent exponential form?

Back

b^c = a

Front

Evaluate log_2(8).

Back

3, because 2^3 = 8.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any base k.

Front

Rewrite as an exponential: log_5(25) = 2

Back

5^2 = 25

Front

What is the logarithm of 1 in any base?

Back

0, because any number raised to the power of 0 equals 1.

Front

Evaluate log_10(1000).

Back

3, because 10^3 = 1000.