2.10 ExpLog - Inverse of Exp and Log - Edubirdie

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2.10 INVERSE OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS RECALL Logarithms and exponents are connected algebraically due to the parts of the expression Exponent: Logarithm: 𝐸 𝐵 =𝑃 𝐸 = log 𝐵 𝑃 2 3 =9 2 = log 3 9 FINDING INVERSE Must switch forms to isolate “y” 𝑓 𝑥 =8 2 𝑥=8 2 3 𝑥−1 3 𝑦−1 −4 −4 𝑥+4 = 2 3 𝑦−1 8 𝐵𝐸 = 𝑃 𝐸 = log 𝐵 𝑃 𝑥+4 3 𝑦 − 1 = log 2 8 1 𝑥+4 𝑦 − 1 = log 2 3 8 1 𝑥+4 𝑦 = log 2 +1 3 8 𝑓 −1 (𝑥) 1 𝑥+4 = log 2 +1 3 8 TRY IT 𝟏 𝒇 𝒙 = 𝟒 𝟕 −𝟐 𝒙− 𝟐 𝟑 + 𝟏𝟏 INVERSE OF LOG 𝟏 𝒇 𝒙 = −𝟑 log 𝟕 𝒙 + 𝟒 − 𝟗 𝟐 TRENDS Base stays the same 𝟏 𝒂𝒊𝒏𝒗𝒆𝒓𝒔𝒆 = 𝒃𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒃𝒊𝒏𝒗𝒆𝒓𝒔𝒆 = 𝟏 𝒂𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒉𝒊𝒏𝒗𝒆𝒓𝒔𝒆 = 𝒌𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒌𝒊𝒏𝒗𝒆𝒓𝒔𝒆 = 𝒉𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 HOMEWORK Visions 1 P185: 8bdf (find inverse, and graph)

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