Solving Exponential and Logarithmic 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, log_b(a) = c means b^c = a.

Front

Convert the logarithmic equation log_6(2x + 3) = 3 to exponential form.

Back

6^3 = 2x + 3.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

Expand the expression: 6log_8(u) - 2log_8(v).

Back

This expression is already in expanded form.

Front

Solve for x: 3^(7x + 2) - 3 = 352,944.

Back

x = 4.

Front

What is the value of log_9(59049)?

Back

5, because 9^5 = 59049.

Front

If log_b(x) = y, what is x in terms of b and y?

Back

x = b^y.

Front

What is the product rule for logarithms?

Back

log_b(mn) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

log_b(m/n) = log_b(m) - log_b(n).

Front

What is the power rule for logarithms?

Back

log_b(m^p) = p * log_b(m).