Logarithms

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 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

Evaluate: log_3(81)

Back

4

Front

Solve for x: 3^x = 27

Back

x = 3

Front

Change to Logarithmic Form: 12^2 = 144

Back

log_12(144) = 2

Front

Evaluate: log_12(1)

Back

0

Front

Evaluate: log_4(16)

Back

2

Front

What is the value of log_b(b)?

Back

1, because any number raised to the power of 1 is itself.

Front

What is the value of log_b(1)?

Back

0, because any base raised to the power of 0 is 1.

Front

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

Back

b^c = a.