Solving Exponential & Logarithmic Equations Lesson Notes

Presentation

•

Mathematics

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9th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.BF.B.5

Standards-aligned

Manuel Rodriguez

Used 52+ times

FREE Resource

34 Slides • 18 Questions

Two forms

1. exponential

2. logaerithmic

It helps to think about logarithms as exponents. Rewriting can help you figure it out.

Rewriting Logarithms

Multiple Choice

Rewrite log₂8 = 3 in exponential form

2⁸ = 3

2³ = 8

3² = 8

8³ = 2

Multiple Choice

Write in exponential form.
log₂32 = 5

2^-5 = 32

2³² = 5

2⁵ = 32

32⁵ = 2

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

log₃4 = 81

log₈₁3 = 4

log₃81 = 4

log₄81 = 3

Multiple Choice

Rewrite log₃81 = 4 exponentially

3⁴= 81

4³= 81

81³=4

Change of Base

Wait... What was that log₇46??

We need a way to go back and forth between base 10 and other bases.

This is called the CHANGE OF BASE formula!

Multiple Choice

Which property of logarithms is demonstrated below:

$\log_920\ =\ \frac{\log20}{\log9}$

Product property

Quotient property

Power property

Change of Base Property

PROPERTIES OF LOGARITHMS

Multiple Choice

Write log_b(xy) as two logs

log_bx+log_by

log_bx-log_by

log_bx*log_by

log_bx/log_by

Multiple Choice

Write log_b(x/y) as two logs

log_bx-log_by

log_bx+log_by

log_bx*log_by

log_bx/log_by

Multiple Choice

Rewrite log_b(xⁿ)

nlog_bx

(log_bx)ⁿ

xⁿlog_bx

log_b(xⁿ)

Multiple Choice

Use the properties of logarithms to retwrite

Multiple Choice

Rewrite as a single logarithm:

$\log3\ +\ \log7$

log 10

log 21

log 3/7

log 3/log 7

Multiple Choice

Rewrite as a single logarithm:

$\log_260\ -\ \log_210$

$\log_26$

$\log_250$

$\frac{\log_260}{\log_210}$

$\log_270$

Multiple Choice

Use the properties of logarithms to rewrite as the sum of two logarithms:

$\log55$

log 40 + log 15

log 50 + log 5

log 11 + log 5

Solving Exponential Equations

Second Method: When there is an exponent on only ONE side.

Multiple Choice

Solve for x. $\log_7x=4$

16384

2401

1.75

Multiple Choice

Solve this one!

$3\cdot4^{x-1}=24$

$x=1$

$x=\frac{\log8}{\log4}+1$

$x=\frac{\log21}{\log4}+1$

$x=1.5$

This is how the last problem should be solved!!

There are 3 Log Properties

Product Property

Echoes the multiplication rule of exponents

A product of 2 expressions within a log can be expanded into a sum of those expressions

Multiple Choice

Expand: log(4x)

log4-logx

log4+logx

4logx

xlog4

Multiple Choice

Rewrite as a single logarithm:

$\log3\ +\ \log7$

log 10

log 21

log 3/7

log 3/log 7

Quotient Property

Echoes the Division Rule of Exponents

When 2 expressions within a log are divided they can be expanded into a difference of those expressions

Quotient Examples

Notice when condensing we write only ONE log term!

Multiple Choice

Expand: $\log\left(\frac{x}{y}\right)$

logx+logy

xlogy

log(x-y)

logx-logy

Multiple Choice

Expand $\log_6\left(\frac{y}{36}\right)$

$\log_6y+\log_636$

$\log_6y-\log_636$

$\log_636+\log_6y$

$\log_636-\log_6y$

Power Property

Examples

Additional rules

Examples

Solving Exponential Equations

1.Rewrite both sides of the equation with the same base.

2.Set the exponents equal to one another.

3.Solve for x.

5^x = 625

5^x = 5⁴

x = 4

Solving Exponential Equations

1.Rewrite both sides of the equation with the same base.

2.Set the exponents equal to one another.

3.Solve for x.

3^2x = 81

3^2x = 3⁴

2x = 4

x = 2

Solving Exponential Equations

1.Rewrite both sides of the equation with the same base.

2.Set the exponents equal to one another.

3.Solve for x.

3^{2x + 1} = 3^{1 - x}

2x + 1 = 1 - x

2x + x = 1 - 1

3x = 0

x = 0

Solving Exponential Equations

1.Rewrite both sides of the equation with the same base.

2.Set the exponents equal to one another.

3.Solve for x.

(⅓)^x = 81

3^-x = 3⁴

-x = 4

x = -4

Solving Exponential Equations

1.Rewrite both sides of the equation with the same base.

2.Set the exponents equal to one another.

3.Solve for x.

9^{2x - 1} = 3^8x

(3²)^{2x - 1} = 3^8x

3^{4x - 2} = 3^8x

4x - 2 = 8x

-2 = 8x + 4x

-2 = 12x

x = -½

Exponential to Logarithmic

5⁰ = 1

log₅1 = 0

2⁵ = 32

log₂32 = 5

3^-2 = 1/9

log₃1/9 = -2

4^x = 16

log₄16 = x

Logarithmic to Exponential

log₄64 = 3

4³ = 64

log₁₄₃20,449 = 2

143² = 20,449

log_bm = n

bⁿ = m

log₂⅛ = -3

2^-3 = ⅛

Two forms

1. exponential

2. logaerithmic

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Solving Exponential & Logarithmic Equations Lesson Notes

Two forms

Change of Base

Wait... What was that log746??

​PROPERTIES OF LOGARITHMS

Solving Exponential Equations

There are 3 Log Properties

Product Property

Quotient Property

Quotient Examples

Power Property

Power Property

Examples

Additional rules

Examples

Two forms

Similar Resources on Wayground

Popular Resources on Wayground

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Wait... What was that log₇46??

PROPERTIES OF LOGARITHMS