Exploring Properties of Logarithms

What does the product property of logarithms state?

• Log of a product is the sum of the logs.

• Log of a power is the exponent times the log.

• Log of a quotient is the difference of the logs.

• Log of a sum does not have a specific property.

How does the quotient property of logarithms work?

• It divides the logs of the base numbers.

• It adds the logs of the numerator and denominator.

• It multiplies the logs of the numerator and denominator.

• It subtracts the log of the denominator from the log of the numerator.

What is the result of applying the power property in logarithms?

• The exponent becomes the coefficient of the log.

• The base of the log is raised to the power of the exponent.

• The log is divided by the exponent.

• The log is multiplied by the exponent.

How can logarithmic equations be solved using their properties?

• By converting them into exponential equations.

• By graphing the logarithmic functions.

• By factoring the logarithmic expressions.

• By applying the properties to simplify and solve for the variable.

What is the first step in solving a logarithmic equation with multiple logs?

• Isolate the logarithmic term on one side.

• Combine all logs into a single logarithmic expression.

• Convert the logarithmic equation into an exponential form.

• Factor the logarithmic equation.

In solving log base 4 of (x^2 - 6x) = 2, what is the base, exponent, and answer respectively?

• 4, 2, x^2 - 6x

• 4, x^2 - 6x, 2

• 2, 4, x^2 - 6x

• x^2 - 6x, 2, 4

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When solving log equations, what does setting two logs equal to each other imply?

• Their exponents are equal.

• The expressions inside the logs are equal.

• Their bases are equal.

• The coefficients of the logs are equal.

What method is used to solve the equation log base 6 of (x^2 + 5x) = 2?

• Converting to exponential form and solving.

• Factoring the expression inside the log.

• Using the quadratic formula.

• Applying the logarithm properties directly.

How do you solve a logarithmic equation with a single log on each side?

• By equating the exponents of the bases.

• By equating the bases of the logarithms.

• By equating the expressions inside the logs.

• By adding the logs together.

What is the correct approach to solve log base 10 of (a^2 + 21a) = 2?

• Factor the quadratic equation inside the log.

• Use the product property to simplify the log.

• Convert the log equation into an exponential equation.

• Apply the power property of logarithms.