Tutorial - Solving logarithmic equations ex 10, log(2x)+log(x-5)=2

The video tutorial explains how to apply properties of logarithms to simplify expressions and solve equations. It covers rewriting logarithmic expressions using the distributive property, converting them into exponential form, and factoring quadratic equations to find solutions. The tutorial also emphasizes checking for extraneous solutions, particularly in the context of logarithms, where the domain is restricted to positive values.

What property of logarithms allows you to combine log base B of X and log base B of Y into a single logarithm?

• Change of Base Property

• Power Property

• Quotient Property

• Product Property

When converting a logarithmic equation to exponential form, what is the base used for common logarithms?

• 5

• 10

• 2

• e

What is the first step in solving the equation 10^2 = 2X^2 - 10X?

• Divide both sides by 10

• Add 100 to both sides

• Subtract 100 from both sides

• Multiply both sides by 2

Which pair of numbers can be used to factor the quadratic equation 2X^2 - 5X - 50?

• 25 and 2

• 5 and 10

• 1 and 50

• 10 and -5

Why is X = -5 considered an extraneous solution in the context of logarithms?

• Because it results in a positive logarithm

• Because it results in a negative logarithm

• Because it is not a real number

• Because it is greater than 10