Logarithmic Functions and Exponential Equations
In this unit, learn how to write and evaluate logarithmic expressions, solve exponential equations using common bases, work with exponential and logarithm equations, understand logarithmic form, and find the inverse of functions. Practice solving equations with various bases and learn to convert between exponential and logarithmic forms effectively.
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Presentation Transcript
Unit 8 [7-3 in text] Logarithmic Functions Today s Objective: I can write and evaluate logarithmic expressions.
Solving exponential equations using common bases 4?= 32 1 16 5?= 125 4?= 2? 5 Write each side with the same base. 2 = 2 1 4?= 2? = 5 ? =5 42 3 5?= 5 2 4?= 4 2 Since bases are the same exponents must be equal. 2?= 7 ? = 2 ? = 3
Exponential & Logarithm Equations Exponential Equation Logarithm Equation Inverse ?log??= ? Exponent/power a = x b = x logb a log???= ? Base Result Common Log: Logs with a base 10 Written log only no base # needed Calculator button: [LOG] Read: log base b of a
? = ?? log?? = ? Write in logarithmic form Write in exponential form 14 = 5? ? log log514 = ? 514 log38 = ? 3 3?= 8 23 = ?? log?23 = ? 52?= 34 log534 = 2? log8(6) + 1 = ? 6 = 103?+1 log106 = 3? + 1 log86 = ? 1 8? 1= 6 log6 = 3? + 1
Solve each equation by using common base method ? = ?? log?? = ? log464 = 2? + 3 ? = log5625 log327 = ? 7 3? 7= 27 42?+3= 64 42?+3= 43 5?= 625 3? 7= 33 5?= 54 2? + 3 = 3 ? 7 = 3 ? = 4 ? = 0 ? = 10
Find the inverse of each function ? = ?? log?? = ? ? = 5log7(? + 4) ? =3? ? = 34?+ 2 4 ? = 5log7(? + 4) ? 5= log7(? + 4) ? = 34?+ 2 ? =3? ? 2 = 34? 4 log3(? 2) = 4? ? 5= ? + 4 4? = 3? 7 log3(? 2) 4 ? 5 4 = ? = ? log34? = ? 7
