Logarithmic Equations and Solutions

Logarithmic Equations and Solutions

Assessment

Interactive Video

Mathematics

7th - 10th Grade

Practice Problem

Hard

CCSS
8.EE.C.7B, HSA.REI.A.1, 6.EE.B.7

+1

Standards-aligned

Created by

Aiden Montgomery

FREE Resource

Standards-aligned

CCSS.8.EE.C.7B
,
CCSS.HSA.REI.A.1
,
CCSS.6.EE.B.7
CCSS.7.EE.B.4A
,
The video tutorial explains how to solve a logarithmic equation using the property that if two logarithms with the same base are equal, their arguments must also be equal. The tutorial provides a step-by-step solution to the equation log base 4 of 6X equals log base 4 of 4x + 5, resulting in x = 2.5. The solution is verified by substituting back into the original equation, confirming the correctness of the solution.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial logarithmic equation given in the problem?

log base 4 of 6X = log base 4 of (5x + 4)

log base 5 of 6X = log base 5 of (4x + 5)

log base 4 of 6X = log base 4 of (4x + 5)

log base 5 of 6X = log base 5 of (5x + 4)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which property of logarithms is used to equate the expressions inside the logs?

Power Property

Product Property

One-to-One Property

Quotient Property

Tags

CCSS.HSA.REI.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the equation for x?

Add 4X to both sides

Subtract 4X from both sides

Divide both sides by 4

Multiply both sides by 4

Tags

CCSS.6.EE.B.7

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After simplifying, what equation do we get before solving for x?

2x = 5

x = 5

4x = 5

6x = 5

Tags

CCSS.7.EE.B.4A

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of x after solving the equation?

x = 3

x = 3.5

x = 2.5

x = 2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of substituting the solution back into the original equation?

To find a new solution

To change the base of the logarithm

To verify the correctness of the solution

To simplify the equation further

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of the left side of the equation after substitution?

log base 4 of 12

log base 4 of 10

log base 4 of 15

log base 4 of 20

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