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

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.

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

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

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

• 128

• 64

• 32

• 16

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

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