Name: 11.2 11.2 Logarithmic Functions EX 1: Convert the following to logarithms or vice-­‐versa. 64 =82 9-­‐2 = 1/ 81 log 7 x = y A. Evaluating Logarithms EX 1: Evaluate the following logarithms: log 3 27 log 5 1 B. Special Properties of Logarithms C. Solving Logarithmic Equations EX 1: Solve the following: log 5 x = 2 log x 64 = 3 Maya Lanzetta log 5 125 = 3 log 2 4 log10 100 log 7 x = −1 log 3 (x + 2) = log 3 5 MAT 122 The invention of logarithms, by shortening the labors, double the life of the astronomer. ~Pierre-Simon Laplace
D. Graphing f (x) = log 5 x E. Applied Problem EX 1: The level of sound Pressure S (in decibels) is defined by S = 20 log10
( ) , where P is the actual sound pressure in P
P0
newtons per square meter (N/m2) and P0 is the threshold of human hearing, which equals 2 x 10-­‐5 N/m2. A sound at the pain threshold has a sound pressure of about 20 N/m2. Calculate the sound pressure level at the pain threshold. Challenge: Solve −4 log 3 − 9y = −4