Summarize:

We know that 10 * 100 = 1000. Written in terms of powers (or logarithms), 101 * 102 = 103. We also know that 1 + 2 = 3. In general, 10x * 10y = 10x + y. So, the sum of the logarithms of two different numbers is the logarithm of the product of those numbers. We can multiply two numbers of the same base by adding their powers. Use the method above to find the logarithms. For example, if you want to multiply 15.27 and 48.54, you would find the log of 15.27 to be 1.1838 and the log of 48.54 to be 1.6861. In this example, add 1.1838 and 1.6861 to get 2.8699. This number is the logarithm of your answer. You can do this by finding the number in the body of the table closest to the mantissa of this number (8699). The more efficient and reliable method, however, is to find the answer in the table of anti-logarithms, as described in the method above. For this example, you will get 741.1.
Understand how to multiply numbers using their logarithms. Look up the logarithms of the two numbers you want to multiply. Add the two logarithms to find the logarithm of the solution. Look up the anti-logarithm of the result from the above step to find the solution.