Tutorial - Solving logarithmic equations ex 11, log4(x+12)+log4(x)=3

Tutorial - Solving logarithmic equations ex 11, log4(x+12)+log4(x)=3

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

The video tutorial covers the properties of logarithms, focusing on the addition of logarithms with the same base and rewriting them as a product. It then applies the distributive property and converts the equation into exponential form. The tutorial proceeds to solve the equation by factoring and using the zero product property. Finally, it discusses extraneous solutions, emphasizing the importance of checking the domain of logarithmic functions to ensure valid solutions.

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5 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What property allows the addition of two logarithms with the same base to be rewritten as a single logarithm of a product?

Distributive Property

Product Property of Logarithms

Quotient Property of Logarithms

Power Property of Logarithms

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can the equation log base 4 of (X^2 + 12X) = 3 be rewritten in exponential form?

X^2 + 12X = 4^3

3^4 = X^2 + 12X

4^3 = X^2 + 12X

X^2 + 12X = 3^4

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of 4^3 in the equation 4^3 = X^2 + 12X?

128

64

32

16

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which pair of numbers multiplies to 64 and adds up to 12 in the equation X^2 + 12X = 64?

12 and 2

16 and -4

10 and 6

8 and 8

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is X = -16 considered an extraneous solution in the context of logarithms?

Because it results in a negative argument for the logarithm

Because it results in a zero base for the logarithm

Because it results in a negative base for the logarithm

Because it results in a zero argument for the logarithm

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