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. It is expressed as log_b(a) = c, meaning 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

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

How do you convert an exponential equation to logarithmic form?

Back

To convert an exponential equation b^c = a to logarithmic form, write it as log_b(a) = c.

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(xy) = log_b(x) + log_b(y).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(x/y) = log_b(x) - log_b(y).

Front

What is the power rule for logarithms?

Back

The power rule states that log_b(x^k) = k * log_b(x).

Front

What is the value of log_2(64)?

Back

log_2(64) = 6, because 2^6 = 64.

Front

How do you solve the equation log_2(x + 5) = 3?

Back

To solve log_2(x + 5) = 3, rewrite it in exponential form: x + 5 = 2^3, so x = 8 - 5 = 3.