Exponential and Logarithmic Equations

Presentation

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Mathematics

•

11th Grade

•

Practice Problem

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Easy

Ana Rizchel Cordero

Used 16+ times

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12 Slides • 21 Questions

Exponential and Logarithmic Equations

by: Ana Rizchel C. De Ocampo

Open Ended

What can be the other examples of EXPONENTIAL GROWTH?

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Exponential Equation

It is one in which a variable occurs in the exponent.

Examples:

2^x = 128

2^{x - 2} = 64

5^{2x - 1} = 625

3^2x = 243

2^{2x - 1} = 4^{3x + 2}

3^x = 48

16^-x = 1/64

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

Multiple Choice

Solve the given exponential equation: 2^x = 64

x = 2

x = 4

x = 6

x = 8

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

Multiple Choice

Solve the given exponential equation: 3^{2x - 3} = 27

x = 3

x = 6

x = 9

x = 27

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

Multiple Choice

Solve the given exponential equation: 8^{x - 8} = 8

x = 1

x = 8

x = 0

x = 9

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

Multiple Choice

Solve the given exponential equation: $2^x=\frac{1}{8}$

x = 3

x = -3

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

Fill in the Blanks

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Logarithmic Equation

It is an equation that involves an expression such as log_bx. We can read it as "logarithm of x with base b" or "log base b of x."

Examples:

log₄16 = x

log₂4 = 2

log₁₀1000 = 3

log₃(x + 4) = 6

Exponential to Logarithmic

5⁰ = 1

log₅1 = 0

2⁵ = 32

log₂32 = 5

3^-2 = 1/9

log₃1/9 = -2

4^x = 16

log₄16 = x

Multiple Choice

Express the given exponential equation in its logarithmic equation:

$6^3=216$

$\log_36=216$

$\log_3216=6$

$\log_63=216$

$\log_6216=3$

Multiple Choice

Express the given exponential equation in its logarithmic equation:

$49=7^2$

$\log_749=2$

$\log_72=49$

$\log_27=49$

$\log_249=7$

Multiple Choice

Express the given exponential equation in its logarithmic equation:

$m^k=5$

$\log_mk=5$

$\log_m5=k$

$\log_5k=m$

$\log_5m=k$

Multiple Choice

Express the given exponential equation in its logarithmic equation:

$3^{\frac{1}{4}}=n$

$\log_3n=\frac{1}{4}$

$\log_3\frac{1}{4}=n$

$\log_n3=\frac{1}{4}$

$\log_n\frac{1}{4}=3$

Multiple Choice

Express the given exponential equation in its logarithmic equation:

$3^{-4}=\frac{1}{81}$

$\log_{-4}3=\frac{1}{81}$

$\log_{-4}\frac{1}{81}=3$

$\log_3\frac{1}{81}=-4$

$\log_3-4=\frac{1}{81}$

Logarithmic to Exponential

log₄64 = 3

4³ = 64

log₁₄₃20,449 = 2

143² = 20,449

log_bm = n

bⁿ = m

log₂⅛ = -3

2^-3 = ⅛

Multiple Choice

Express the given logarithmic equation in its exponential equation:

$\log_77=1$

$1^7=7$

$7^1=7$

$7^7=1$

Multiple Choice

Express the given logarithmic equation in its exponential equation:

$\log_{25}5=\frac{1}{2}$

$25^5=\frac{1}{2}$

$25^{\frac{1}{2}}=5$

$5^{\frac{1}{2}}=25$

$5^{25}=\frac{1}{2}$

Multiple Choice

Express the given logarithmic equation in its exponential equation:

$\log_2\frac{1}{64}=-6$

$2^{-6}=\frac{1}{64}$

$-6^2=\frac{1}{64}$

$-6=2^{\frac{1}{64}}$

$2=-6^{\frac{1}{64}}$

Multiple Choice

Express the given logarithmic equation in its exponential equation:

$\log_xy=\frac{1}{w}$

$y^{\frac{1}{w}}=x$

$y^x=\frac{1}{w}$

$x^{\frac{1}{w}}=y$

$x^y=\frac{1}{w}$

Multiple Choice

Express the given logarithmic equation in its exponential equation:

$\log_2\sqrt[3]{2}=\frac{1}{3}$

$\sqrt[3]{2}=2^{\frac{1}{3}}$

$\frac{1}{3}^2=\sqrt[3]{2}$

$2^{\sqrt[3]{2}}=\frac{1}{3}$

$2^{\frac{1}{3}}=\sqrt[3]{2}$

Evaluating Logarithms

Examples:

log₃27

x = log₃27

3^x = 27

3^x = 3³

x = 3

log₃27 = 3

log₅625

x = log₅625

5^x = 625

5^x = 5⁴

x = 4

log₅625 = 4

Evaluating Logarithms

Examples:

log₅5√5

x = log₅5√5

5^x = 5√5

5^x = 5 ⋅ 5^½

5^x = 5^3/2

x = 3/2

log₁₀0.01

x = log₁₀0.01

10^x = 0.01

10^x = 10^-2

x = -2

log₁₀0.01 = -2

log₅5√5 = 3/2

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Exponential and Logarithmic Equations

by: Ana Rizchel C. De Ocampo

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