Algebra 2 Ch.8 Notes Page 61 P Logarithmic Functions as Inverses

Logarithms (Logs) The Log to the base b of a positive number y is defined as... The log of a negative number or zero is undefined. If y = b x, then log b y = x log base b of y b ≠ 0 b > 1 y = b x log b y = x A common log is a log that uses base 10. You can write the common log log 10 y as log y

Writing in Logarithmic Form 25 = 5 2 y = b x log b y = x 729 = 3 6 1/8 = (1/2) = = 64

Evaluating Logarithms Evaluate log 8 16 Write an equation in log form Convert to exponential form Write each side using base 2??? Use Power Property of Exponents Set the Exponents equal Solve for x log 3 81 log 64 1/32 log 9 27 log

Families of Logarithmic Functions Parent Function:y = log b x Stretch ( | a | > 1 ) Shrink ( 0 < | a | < 1 )y = alog b x Reflection ( a < 0 ) in x-axis Translation:y = log b (x - h) + k (horizontal by h)(vertical by k) Combined:y = alog b (x - h) + k

Logarithmic Functions and Graphs A logarithmic function is the inverse of an exponential function. y = 10 x Write in Exponential Form Switch x and y log 10 y = x log 10 x = y y = 10 x is the inverse of y = log 10 x

Graphing Logarithmic Functions Graph y = log 2 x

Translating y = log b x Graph y = log 6 (x - 2) + 3 (x + 2) (y + 3)

HW # P450 #6,10-12,14-17,19,20,22,24,35,64,67,68 Please put your name and class period at the top of the homework. Also include the homework number.

Earthquake Energy Release (Destructive Power)

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