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## Solving Exponential Equations (Lacking a Common Base)

#### High School Algebra - HSF-LE.A.4

How to Solve Exponential Equations That Lack a Common Base - We all know how to solve basic algebra, separate the variable and solve for it. There are various different ways that you can use to solve algebraic equations including completing-squares, middle-term breaking, quadratic formula. However, things get challenging when in an algebraic equation, the variable is in the exponent. Such equations are what we term as exponential equations. There are two types of exponential equations, one where the bases are same and the second one where the bases are not same. When we are dealing with exponential equations where the bases are not same, we bring log into use. Example: Solve for x, 3x = 11 | You can start solving this by taking logarithm on both sides. As logarithm must have a base, you can choose the base of the exponential equation. In this case, we can take 3 as the base of the logarithmic function. log3⁡ 3x = log3⁡ ⁡11 | xlog3⁡ ⁡3 = log3⁡ ⁡11 | On solving this equation further, we get x=2.183. You can now substitute the value of x into the exponential function to find the final answer. These worksheets and lessons help students learn how to approach slightly more complex trig. problems.