Laws of Logarithm

Presentation

•

Mathematics

•

10th - 11th Grade

•

Hard

Joseph Anderson

FREE Resource

18 Slides • 18 Questions

Solving Logarithmic Equations

By Dr KEE CH

Learning objectives:

1. Students will be able to solve logarithmic equations using the laws of logarithms.

2. Students will be able to demonstrate the seven laws of logarithms confidently.

3. Students will be able to conceptualize logarithmic functions as inverse of exponential functions.

Law 1: Product Rule

log_b(M⋅N)=log_bM+log_bN

Draw

Expand $\log_3\left(27x^2y^5\right)$

Draw

Expand $\log_212w^5\sqrt[]{y}$

Law 2: Quotient Rule

log_b(M/N)=log_bM-log_bN

Draw

Evaluate $\log_3162-\log_32$

Law 3: Power Rule

log_b(M^k)= k⋅log_bM

Draw

Evaluate $\log_28$

Draw

Evaluate $\log_28+\log_24$

Wait! There's more...

Not really a "law" but useful to know

log_b(1)= 0

Not really a "law" but useful to know

log_b(b)= 1

Not really a "law" but useful to know

log_b(b^k)= k

Not really a "law" but useful to know

b^logb(k)= k

Change of Base Rule

log_ba=log_x b / log_xa

Draw

Evaluate $\log_58$ by changing the base to $\log_{10}$

How to solve logarithmic equation?

log₃x = log₃7 + log₃3

If log₁₀8 = x and log₁₀3 = y

Express log₁₀24 in terms of x and y only

If log₁₀8 = x and log₁₀3 = y

Express log₁₀720 in terms of x and y only

You try!

Check your understanding

Multiple Choice

If 3^x = y, which of the following is true?

log₃y = x

log₃x = y

log_xy = 3

log_y3 = x

Multiple Choice

If log_a8 = b, which of the following is true?

a^b = 8

b^a = 8

a⁸ = b

8^b = a

Multiple Choice

Simplify log(12) + log (6)

log(72)

log(18)

log(6)

log(2)

Multiple Choice

Simplify: log(3) + 2log(5)

log(75)

2log(15)

log(30)

log(13)

Multiple Choice

Simplify: 2log(x) + 3log(xy)

log(x⁵y³)

log(5xy)

5log(x²y)

log(6x²y)

Multiple Choice

Simplify: log(24) - log(8)

log(3)

log(16)

4log(2)

-log(32)

Multiple Choice

Simplify: log(16) - 3log(2)

log(2)

log(10)

-3log(8)

3log(14)

Multiple Choice

Simplify: 3log(xy) - 2log(x)

log(xy³)

log(y)

1.5log(x²y)

Can't be simplified

Multiple Choice

What is the most simple answer possible:
log_x(x³y) - log_x(xy)

log_x(x²)

log_x(x⁴-y²)

Multiple Choice

Solve for x:
log(3x-1) - log(5) = 2

x = 167

x = 500

x = 2

x = 3.67

Draw

Evaluate $\log_5500-2\log_52+\log_432+\log_48$

Draw

Expand $\log_7\left(\frac{49m^6}{k^3}\right)$

Solving Logarithmic Equations

By Dr KEE CH

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