how to solve logs
Subject:
Algebra [1]
1. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.
Example 1: Solve for x in the equation Ln(x)=8.
Solution:
Step 1: Let both sides be exponents of the base e. The equation Ln(x)=8 can be rewritten .
Step 2: By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written x. The equation can now be written .
Step 3: The exact answer is
and the approximate answer is
Check: You can check your answer in two ways. You could graph the function Ln(x)-8 and see where it crosses the x-axis. If you are correct, the graph should cross the x-axis at the answer you derived algebraically.