Solving Logarithmic Equations Challenge

What must be true for two logarithms on either side of an equation to be considered equal?

• They must have different bases.

• Their exponents must be equal.

• Their bases must be the same and their arguments equal.

• They must both be greater than one.

What is the first step in solving an equation that contains a single logarithm?

• Isolate the logarithm on one side of the equation.

• Multiply both sides by the base of the logarithm.

• Add the logarithm to both sides of the equation.

• Convert the logarithm to an exponential form immediately.

What does exponentiating both sides of an equation involving a logarithm accomplish?

• It converts all terms into their exponential counterparts.

• It eliminates the logarithm by using its inverse property.

• It simplifies the logarithm into a linear equation.

• It balances the equation by making both sides equal.

What is the purpose of isolating the logarithm in an equation?

• To convert the logarithm to an exponential form.

• To prepare the equation for exponentiation.

• To simplify the calculation of the base.

• To make the equation easier to graph.

When a logarithm is multiplied by a constant in an equation, what should be done first?

• Divide both sides by the constant.

• Subtract the logarithm from both sides.

• Exponentiate both sides immediately.

• Add the constant to both sides.

What is the base used for exponentiation when solving an equation with a natural logarithm?

• Any number that is convenient.

• 10

• The base of the natural logarithm (e)

• 2

How are logarithms that are being added combined into a single logarithm?

• By dividing their arguments.

• By multiplying their arguments.

• By adding their exponents.

• By subtracting their bases.

What does a negative exponent signify when condensing logarithms?

• The logarithm should be divided by its base.

• The base of the logarithm becomes negative.

• The argument of the logarithm should be squared.

• The argument of the logarithm moves to the denominator of a fraction.

What mathematical process is used when two fractions are set equal to each other?

• Dividing

• Simplifying

• Cross-multiplying

• Factoring

What should students do after attempting practice problems 9 and 10?

• Check their answers with the teacher.

• Move on to the next chapter.

• Repeat the video from the beginning.

• Write a summary of what they learned.