Logarithmic & Exponential Equations

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, if b^y = x, then log_b(x) = y.

Front

What is the relationship between logarithmic and exponential functions?

Back

Logarithmic functions are the inverses of exponential functions. If y = b^x, then x = log_b(y).

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

How do you solve the equation log_b(x) = y for x?

Back

To solve log_b(x) = y, rewrite it in exponential form: x = b^y.

Front

What is the product rule for logarithms?

Back

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

Front

How do you convert an exponential equation to a logarithmic equation?

Back

To convert an exponential equation of the form b^y = x to logarithmic form, write it as log_b(x) = y.

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Front

What is the value of log_4(64)?

Back

log_4(64) = 3, because 4^3 = 64.