Logarithms

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. It is expressed as log_b(a) = c, meaning b^c = a.

Front

Change to Exponential Form: log_3(81) = 4

Back

3^4 = 81

Front

Write in logarithmic form: 10^3 = 1000

Back

log_10(1000) = 3

Front

What is the product rule of logarithms?

Back

The product rule states that log_b(mn) = log_b(m) + log_b(n).

Front

What is the quotient rule of logarithms?

Back

The quotient rule states that log_b(m/n) = log_b(m) - log_b(n).

Front

What is the power rule of logarithms?

Back

The power rule states that log_b(m^p) = p * log_b(m).

Front

Change to Exponential Form: log_5(25) = 2

Back

5^2 = 25

Front

Write in logarithmic form: 2^4 = 16

Back

log_2(16) = 4

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

Condense: log_2(4) + log_2(8)

Back

log_2(32)