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How to Calculate Logarithmic Expression

Logarithms may be thought of as the opposites of exponents, just like subtraction is the opposite of addition. An exponent may be described as a number raised to a power. Calculating or solving a logarithmic equation requires a basic understanding of arithmetic and algebra. One way to think of logarithms, where ^ means "raised to," is that y = b^x is the equivalent of log (base b)(y) = x.

Instructions

- 1
  Write out the logarithmic expression onto a piece of paper. Identify the components of the logarithmic expression. For example, you are given log (base 10)(y) = 4.5, and asked to solve for y. You know that b is 10, x is 4.5 and y is unknown.
- 2
  Rearrange the logarithmic equation so that it is in the form of an exponent. That is, rearrange the logarithm so that it is in the form y = b^x. In the example, y = 10^4.5.
- 3
  Solve the converted exponential equation. In this example, y equals 10 raised to the 4.5th power, which means that you multiply 10 by itself 4.5 times. Therefore, y = 31,622.78.

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