Identify the type of logarithm you need
Write the logarithm in the form ( log_b(x) = y )
Convert to exponential form: ( b^y = x )
Use log rules if simplifying
Apply the product rule: ( log_b(MN) = log_b(M) + log_b(N) )
Apply the quotient rule: ( log_b(M/N) = log_b(M) – log_b(N) )
Apply the power rule: ( log_b(M^k) = klog_b(M) )
Use change of base if needed: ( log_b(x) = frac{log_a(x)}{log_a(b)} )
Check that the argument is positive
Check that the base is positive and not equal to 1
Solve for the unknown if the log is part of an equation
Verify the result by substituting back