Converting Between Forms

Pre-Calculus · Axiom Academy

LESSON Converting Between Forms Exponential and logarithmic notation say the same thing two ways — learn the swap that carries you between them. The exponential form b^ y =x and the logarithmic form are two sides of the same coin — both encode the relationship between the same three numbers. Watch 2^ 3 =8 rearrange into : the base stays put , while the exponent and the result swap places. Exponential form — "2 raised to the 3rd power is 8" Logarithmic form — "the power of 2 that gives 8 is 3" 2. The Three Parts, and Where They Go Every exponential / logarithmic relationship has exactly three parts. Once you can name them, converting is just placing each part into its slot in the other form. The number being raised to a power. It is the base of the exponential and the subscript of the log — it never moves. The power the base is raised to. In the log form this same number becomes the value of the logarithm. The answer when you compute b^ y . In the log form it becomes the argument — the number you take the log of. base base, exponent log value, result argument. That is the entire conversion. 3. The Logarithm Is the Exponent Here is the memory trick that makes conversion automatic: a logarithm asks "what exponent?" literally means "how many factors of 2 multiply to 8 ?" Multiply 2 's one at a time — — and count the steps. You land on 3 , which is exactly the exponent in 2^ 3 =8 . The log's value IS the exponent you needed

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