LEQ: HOW DO YOU EVALUATE COMMON LOGARITHMS? Common Logarithms Sec. 9-5

The inverse of y = 10 x Switch x and y  x = 10 y To solve for y, we define a new function Definition: y is the logarithm of x to the base of 10, or log of x to the base 10 written if and only if 10 y = x. Therefore, the inverse of f(x) = 10 x can be written  x = 10 y  y = log 10 x  f -1 (x) = log 10 x

Common Logarithms Logarithms with base 10 Often write common logs without indicating the base  log 10 x = log x A common logarithm is the exponent to which 10 is raised to get the desired value Can evaluate common logs for any positive real number  To evaluate a common log, write the number with base 10  The exponent on 10 is the common log

Evaluating Common Logarithms Without a calculator:  1.) log 100  = log 10 2  = 2  2.) log.1  = log (1/10)  = log  = -1  3.)  

Common Logarithm Function Is the inverse of the exponential function  Reflections of each other over the line y = x. Domain: the set of positive real numbers Range: the set of all real numbers Never touches the y-axis  The y-axis is an asymptote of the graph The x-intercept is 1

Solving Logarithmic Equations Use the definition of common logarithms Solve log x = 1.5  By definition, x =  Therefore, x ≈ 31.62

Your Turn Lesson Master 9-5A #1-6, 8, 10, 13-15

Homework Pgs #2-4, 6-25, 28, 29