Honors Pre-Calculus A, 2nd Hour, Winter 2016: inverse property

Showing posts with label inverse property. Show all posts

Showing posts with label inverse property. Show all posts

Friday, February 5, 2016

3.4 Solving Exponential and Logarithmic Equations

Introduction

There are two basic strategies you can use to solve these equations.

One-to-One Properties

if and only if x=y

if and only if x=y

Inverse properties

Examples of Exponential Equations:

Can be we written as:

By the one-to-one property, x=5

x=ln 7 by the Inverse property

Solving an Exponential Equation in Quadratic Form

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This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

or

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

x = 0

Solving Logarithmic Equations

ln x = 2

Exponentiate each side

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This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

Final Answer Without a Calculator

Solving a Logarithmic Equation

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Isolate the log (divide both sides by 2)

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Exponentiate both side (by base 5)

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Use the inverse property

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Change-of-Base Formula

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