Use the definition: if ( log_b(x) = y ), then ( b^y = x )
Rewrite the logarithm as an exponential equation
Solve for the exponent
Check that the base is positive and not equal to 1
Check that the argument is positive
Use log properties when needed:
( log_b(MN) = log_b(M) + log_b(N) )
( log_b!left(frac{M}{N}right) = log_b(M) – log_b(N) )
( log_b(M^k) = klog_b(M) )
( log_b(b) = 1 )
( log_b(1) = 0 )
Use common special values:
( log_b(b^k) = k )
( log_{10}(10^k) = k )
( ln(e^k) = k )
If the base is not convenient, use change of base:
( log_b(x) = frac{log(x)}{log(b)} )
( log_b(x) = frac{ln(x)}{ln(b)} )
Simplify the expression before evaluating
Substitute known values and compute the result
Verify the final answer satisfies the original logarithm