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Solving Exponential & Logarithmic Equations



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In this section, we learn how to solve exponential and logarithmic equations. We previously learned how to solve exponential equations when the bases were the same. What techniques can we use to solve an exponential equation when the bases are not the same? We can take the log of both sides, and then utilize the power rule of logarithms to bring the variable out of the exponent. We can then proceed to isolate the variable. When we work with logarithmic equations, we come across two different scenarios. In the first scenario, we are given a logarithm on one side and a number on the other. For this case, we can convert the logarithmic equation into exponential form and then solve the equation. In the second scenario, we end up with a logarithm on each side of the equation. For this case, when the base of each logarithm is the same, we can set the arguments of the logarithms equal to each other and solve for the unknown. When working with exponential and logarithmic equations, we must pay close attention to restricted values. If we obtain a restricted value as a solution, it must be rejected.
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