8-3 Logarithmic Functions as Inverses

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Presentation transcript:

8-3 Logarithmic Functions as Inverses 10/19/17

A logarithm is the inverse to an exponential function. 23 = 8 written as a logarithm is: log2 8 = 3. Log2 8 = x is an equation that is basically asking, “2 to what power is 8?” When you see log2 8 = x, think: 2x = 8 Log2 8 is read “the log of 8 base 2” or “the log base 2 of 8” General form: logb y = x means bx = y Logs are very useful in science & mathematics, especially calculus (the “natural” log (base e). Uses of logs you may have heard of but didn’t realize they were logs: the Richter scale, decibels, pH, & musical intervals. Let’s evaluate some logarithms…

Evaluate: log3 9 = x x = 2 (since 32 = 9) log2 32 = x x = 5 (since 25 = 32) log9 729 = x x = 3 (since 93 = 729) log10 1000 = x x = 3 (since 103 = 1000) log10 10 = x x = 1 (since 101 = 10) Logs base 10 are called the common log. A log with no base written is understood to be base 10. log .1 = x x = -1 (since 10-1 = .1)

Assignment: Page 442 #6 – 25 Write in logarithmic form: 53 = 125 Evaluate: 102 = 100 log 100 = 2 log64 1/32 = ? 64x = 1/32 24 = 16 log2 16 = 4 (26)x = 2-5 same base!! 54 = 625 log5 625 = 4 26x = 2-5 6x = -5 x = -5/6 Assignment: Page 442 #6 – 25