Using a Calculator with Logarithms – Exponential Equations and Change of Base Formula

Exponential Equations and Change of Base Formula

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The problems in this lesson involve solving exponential equations that require a calculator, and evaluating logarithms using the change of base formula. For example, to solve an exponential equation like 5^x = 2, notice that we can't find a like base for 5 and 2, so we first take the log of both sides of the equation, to get log 5^x = log 2. Next, we use our logarithm rule to move the x out in front of the logarithm, and we have have x log 5 = log 2. Finally, we divide both sides by log 5, and we have x = 0.431. The other types of problems in this lesson involve the change of base formula, which states that log base a of x = log x over log a. It's called the change of base formula because the base of a in the original logarithm is changed to the common logarithm base of 10. (When there's no base shown, we can assume the base is 10.) For example, we use the change of base formula to find that log base 3 of 8 simplifies to log 8 over log 3, or 1.893.
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