07.03 Notes.docx

# You can confirm this fact by using the change of base

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You can confirm this fact by using the Change of Base Formula. The Power Property of Logarithms may be summarized with the following algebraic equation. Power Property of Logarithms log b x y = y log b x Summary—Logarithmic Properties Equality Property: log b x = log b y ↔ x = y ex) log 5 x + 2 = log 5 12 then x + 2 = 12 Product Property: log b x + log b y = log b xy ex) log 4 3 + log 4 (x + 2) = log 4 [3(x + 2)] Quotient Property: log b x − log b y = log b x/y ex) log 3 5x − log 3 z = log 3 5x/z Power Property: log b x y = ylog b x ex) log 7 5 x = xlog 7 5 Solving Logarithmic Equations with Constants Up until now, you’ve only been working with equations where each term contains logarithms. Do you remember how to solve logarithmic equations such as log 7 x = 3?

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Notice that the 3 on the right side of the equation is not a logarithm. But you learned how to solve this equation by converting it into an exponential equation. Remember BNE BEN (base-number-exponent –> base-exponent-number)? log 7 x = 3 7 3 = x 343 = x When you encounter a logarithmic equation where constants are involved, isolate the constants on one side. Isolate the logarithms on the other side. Then, turn the logarithmic equation into an exponential equation.
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