Exponential/Logarithmic Function Understanding

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. For example, if b^y = x, then log_b(x) = 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 condense logarithmic expressions?

Back

Use the properties of logarithms: log_b(m) + log_b(n) = log_b(m*n) and log_b(m) - log_b(n) = log_b(m/n).

Front

What is the exponential form of a logarithmic equation?

Back

If log_b(a) = c, then the exponential form is b^c = a.

Front

What is the product property of logarithms?

Back

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

Front

What is the quotient property of logarithms?

Back

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

Front

What is the power property of logarithms?

Back

The power property states that log_b(m^k) = k * log_b(m).

Front

How do you expand the logarithmic expression log_b(m^k * n)?

Back

Using the product property: log_b(m^k * n) = log_b(m^k) + log_b(n) = k * log_b(m) + log_b(n).

Front

What is the value of log_2(8)?

Back

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

Front

How do you approximate logarithms using a calculator?

Back

Use the change of base formula: log_b(a) = log(a) / log(b) using common or natural logarithms.