Logarithms

Front

What is a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another 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

Rewrite the equation 100 = 10^2 in logarithmic form.

Back

log_10(100) = 2.

Front

What is the product rule for logarithms?

Back

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

Front

What is the quotient rule for logarithms?

Back

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

Front

What is the power rule for logarithms?

Back

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

Front

Convert log_2(32) to exponential form.

Back

2^5 = 32.

Front

Simplify log_2(800) - log_2(100).

Back

log_2(800 / 100) = log_2(8) = 3.

Front

What is the value of log_10(1)?

Back

log_10(1) = 0, because 10^0 = 1.

Front

What is the value of log_b(b)?

Back

log_b(b) = 1, because b^1 = b.