Mastering Logarithmic Equations

What are the two main steps in solving log equations?

• Divide both sides by the log base

• Use log properties and solve for x

• Simplify the equation and rewrite it in exponential form

• Isolate the variable and apply the quadratic formula

What is the result of 3 to the fifth power in the process of solving the log equation?

• 216

• 125

• 343

• 243

What is the base of the log in the first example problem?

• 5

• 3

• 10

• 2

How can multiple log terms on the same side of an equation be simplified?

• By dividing the arguments

• By adding the bases

• By multiplying the arguments

• By subtracting the log terms

What happens when you have log base 2 of x equals log base 2 of y?

• x is always greater than y

• x equals y

• x is always less than y

• It's an undefined equation

What indicates an extraneous solution in a log equation?

• A negative exponent

• A zero in the log base

• A positive base

• A negative argument in the log

Why is it important to check solutions in log equations?

• To ensure the base is correct

• To verify there are no extraneous solutions

• To make sure the log argument is not zero

• To confirm the exponent is positive

What method is used to solve the challenging log problem mentioned?

• Factoring

• Quadratic formula

• Graphing

• U-substitution

What does 3 to the negative first power equal?

• 0

• 1/3

• -3

• 3

What is the purpose of using a u-substitution in solving log equations?

• To convert the equation into a quadratic form

• To eliminate the log term

• To determine the base of the log

• To simplify the equation for graphing