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Exponential and Logarithmic Equations

log2(x +1)−log2(2−x) = 3 log 2 ( x + 1) − log 2 ( 2 − x) = 3 Solution. log4(−x) +log4(6 −x) = 2 log 4 ( − x) + log 4 ( 6 − x) = 2 Solution. log(x) =2 −log(x−21) log. ⁡. ( x) = 2 − log.

Solving Logarithmic Equations

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Logarithmic Equations – examples of problems with solutions

Let’s take a look at a couple of examples. Example 1 Solve each of the following equations. 2log9(√x)−log9(6x−1) = 0 2 log 9 ( x) − log 9 ( 6 x − 1) = 0 logx+log(x −1) = log(3x

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Logarithmic Equations

The one-to-one property of logarithmic functions tells us that, for any real numbers x > 0, S > 0, T > 0 and any positive real number b, where b ≠ 1, logbS = logbT if and only if S = T. For example, If log2(x−1) = log2(8),then x−1 = 8. So

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