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## Logarithmic Equations

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

How to Solve Logarithmic Equations? Solving logarithmic functions is a challenge for many students. Before you start solving a logarithmic function, you need to understand its types. There are generally two types of logarithmic functions. The first type looks like logb⁡M = logb⁡N -> M = N The second type looks like logb M = N -> M = bN To solve logarithmic functions, you have to follow some rules; Product Rule: logb⁡(m×n)= logbm + logb ⁡n Quotient Rule: logb (m/n)= logb ⁡m - logb n You can use this information to solve logarithmic functions. Example: Solve 3=log2⁡x + log25 When you see the equation, you can immediately spot the product rule being applied on it. So, you use the product rule to simplify the equation. 3 = log2⁡(x+5) We can now apply the type 2 logarithmic function here and the equation becomes; 23 = x+5 | 8 = x + 5 | x = 3 This is how you can use the type 1, type 2, and both rules to solve a logarithmic function. These worksheets and lessons will help students learn to solve for unknowns within logarithmic equations.