1Cademy - Try It 10.81 and 10.82: Solving $$7^x = 43$$ and $$8^x = 98$$

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Exponential Equation

Example

Try It 10.81 and 10.82: Solving $7^x = 43$ and $8^x = 98$

Practice solving exponential equations by taking the common logarithm of both sides. For the equation $7^x = 43$ , applying the logarithm gives $\log 7^x = \log 43$ . Use the Power Property of Logarithms to rewrite it as $x \log 7 = \log 43$ . Dividing by $\log 7$ provides the exact solution $x = \frac{\log 43}{\log 7}$ , which is approximately $1.933$ . For the equation $8^x = 98$ , taking the logarithm of both sides results in $\log 8^x = \log 98$ . Applying the Power Property yields $x \log 8 = \log 98$ . Dividing by $\log 8$ gives the exact solution $x = \frac{\log 98}{\log 8}$ , which approximates to $2.205$ .