How Do You Convert From Log to Exponential Form?

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Converting logarithms to exponential form is a matter of knowing which symbols represent which part of the equation and directly substituting. This conversion can be done in under a minute, and a calculator is only useful if you want to check your answer.

  1. Understand the components of a logarithm

    A logarithm is the opposite of an exponential expression. An exponent gives a product created by raising a base to a certain power; a logarithm determines to what power a base must be raised to produce a given value. If b^x = y, then logb(y) = x. In the exponent equation, b is the base, x is the exponent, and y is the product created; in the logarithm, b is still the base, y is called the argument, and x is the answer.

  2. Figure out which values you have

    Not all exponents or logarithms are given as full equations. Many logarithms will be given without an answer. For example, you might have log2(8) but not an answer. In this case, you have the base (2) and the argument (8), which is the product in exponent form. Alternatively, you might be given an equation with variables, such as log27(x) = 2/3.

  3. Substitute the values

    Take the constants in the logarithm, and rewrite them as an exponential expression. For any unknowns or variables, use a variable. For example, log2(8) can be written in to the equation log2(8) = x, where 2 is the base and x will be the exponent. 2^x = 8, meaning that x=3. log27(x) = 2/3 can be rewritten as 27^(2/3) = x = 9.