Converting Exponential to Logarithmic

Pre-Calculus · Axiom Academy

EXAMPLE Converting Exponential to Logarithmic Rewrite exponential equations b^ y =x in logarithmic form , one part at a time. Every exponential equation b^ y =x says the same thing as a logarithm: . The base b stays the base, the result x becomes the argument, and the exponent y becomes the value of the log. Rewrite each of these four equations in logarithmic form: 3^ 4 =81 , 5^ 2 =25 , 10^ 3 =1000 , and . Nice work — you converted four exponential equations into logarithmic form by tracking where each part goes. The pattern: b^ y =x becomes — the base stays the base, the result becomes the argument, and the exponent becomes the answer. Base 10: the common log is written as with no subscript, so 10^ 3 =1000 becomes . Base e : the natural log is written as , so becomes . Exponential and logarithmic forms are two views of the same relationship — reading one off the other is the heart of working with logarithms.

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