Unit V: Logarithms Solving Exponential and Logarithmic Equations

Date: 3/19/13

Objective: SWBAT apply properties of exponential functions and will

apply properties of logarithms.

Bell Ringer:

HW Requests: Solving Exponential Equations Worksheet and Log Equations WS from Friday

Homework: Solve Log and Exponential Eqns using logs WS Read section 3.2 Announcements: Chapter 3 Test Friday. Break Packet available online Friday (ACT Prep) State Champions

Logs and Exponentials of the same base are inverse functions of each other they "undo" each other. Swap x and y to find inverse. Logs and Exponentials are opposites.

2log2 5 = 5

log3 37 = 7

Remember that:

f x ax f 1x loga x

f f 1 x and f 1 f x

This means that:

f f 1 aloga x x

inverses "undo" each each other

f 1 f loga ax x

Common Log and Natural Log Exponential function and Natural Log are inverse functions

Solving Exponential and Logarithmic Equations

Section 4.4

JMerrill, 2005 Revised, 2008

Same Base

Solve: 4x-2 = 64x

4x-2 = (43)x

4x-2 = 43x

x?2 = 3x

-2 = 2x

-1 = x

64 = 43 If bM = bN, then M = N

If the bases are already =, just solve the exponents

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