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Mastering Change-of-Base Formulas for Logarithms

Learn to solve logarithmic equations efficiently using the change-of-base formula. Explore examples and practical applications step by step.

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Mastering Change-of-Base Formulas for Logarithms

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  1. Change of Base

  2. There is an answer to this and it must be more than 3 but less than 4, but we can't do this one in our head. (2 to the what is 8?) Let's put it equal to x and we'll solve for x. Change to exponential form. (2 to the what is 16?) use log property & take log of both sides (we'll use common log) (2 to the what is 10?) use 3rd log property Check by putting 23.32 in your calculator (we rounded so it won't be exact) solve for x by dividing by log 2 use calculator to approximate

  3. LOG LN If we generalize the process we just did we come up with the: Example for TI-83 Change-of-Base Formula The base you change to can be any base so generally we’ll want to change to a base so we can use our calculator. That would be either base 10 or base e. “common” log base 10 “natural” log base e

  4. Use the Change-of-Base Formula and a calculator to approximate the logarithm. Round your answer to three decimal places. Since 32 = 9 and 33 = 27, our answer of what exponent to put on 3 to get it to equal 16 will be something between 2 and 3. put in calculator

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