Section 6.6 Solving Exponential and Logarithmic Equations Honors Algebra 2 Section 6.6 Solving Exponential and Logarithmic Equations

Exponential equations-equations in which the variable expressions occur as exponents Logarithmic equations-equations that involve logarithms of variable expressions

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In an equation, if two bases (≠1) are set equal to each other, the exponents must be equal. 𝑏 𝑥 = 𝑏 𝑦 𝑥=𝑦 Sometimes you can get non-equal bases to be the same base.

Solve for x. #1 3 𝑥 = 3 8 #2 4 2𝑥−1 = 4 9 #3 5 𝑥 = 125 20 #4 6 8 = 1 216 3𝑥 #5 2 2𝑥+2 = 32 7𝑥

In an equation in ben form (with the variable in the exponent), write in log form. Isolate the base before writing in log form. 𝑏 𝑥 =𝑛 𝑥= log 𝑏 𝑛

Solve for x #1 3 𝑥 =23 #2 7 2𝑥 =30 #3 4 (5) 𝑥 =100

If you have a single log on each side of the equation (with the same base), you can drop off the logs. log 𝑏 𝑚 = log 𝑏 𝑛 𝑚=𝑛

Solve for x #1 log 4 2𝑥 = log 4 38 #2 log 7 (10𝑥−9) = log 7 (𝑥+10) #3 log 4 𝑥 + log 4 (𝑥−1) = log 4 12

Getting rid of logs! If you have a log on one side and a number on the other side, change “log form” to “ben form”

Solve for x #1 log 2 𝑥 =6 #2 log 3 (𝑥−6) =10 #3 log 4 𝑥 + log 4 (𝑥−12) =3

Newton’s Law of Cooling For a cooling substance with an initial temperature 𝑇 0 , the temperature after t minutes can be modeled by 𝑇= 𝑇 0 − 𝑇 𝑅 𝑒 −𝑟𝑡 + 𝑇 𝑅 where 𝑇 𝑅 is the room temperature and r is the cooling rate of the substance.

Your sister is cooking her famous chili Your sister is cooking her famous chili. When she takes it off the stove, the temperature is 212℉. The room temperature is 75℉, and the cooling rate of chili is r=0.051. How long will it take to cool the chili to a serving temperature of 95℉?

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Assignment #28 Pg. 338 #5-17 odd, 19, 23-33 odd, 37-41 odd