Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which property of logarithms does this equation demonstrate? \newlinelog⁡33+log⁡36=log⁡318\log_3 3 + \log_3 6 = \log_3 18\newlineChoices:\newline(A) Product Property\text{Product Property}\newline(B) Power Property\text{Power Property}\newline(C) Quotient Property\text{Quotient Property}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Identify properties of logarithmsright chevron icon

Full solution

Q. Which property of logarithms does this equation demonstrate? \newlinelog⁡33+log⁡36=log⁡318\log_3 3 + \log_3 6 = \log_3 18\newlineChoices:\newline(A) Product Property\text{Product Property}\newline(B) Power Property\text{Power Property}\newline(C) Quotient Property\text{Quotient Property}
  1. Analyze the equation: Analyze the given equation.\newlineWe have the equation log⁡33+log⁡36=log⁡318\log_3 3 + \log_3 6 = \log_3 18. We need to determine which logarithmic property this equation represents.
  2. Recall logarithmic properties: Recall the properties of logarithms.\newlineThere are three main properties of logarithms that are relevant to this problem: the Product Property, the Power Property, and the Quotient Property. The Product Property states that log⁡b(P)+log⁡b(Q)=log⁡b(PQ)\log_b (P) + \log_b (Q) = \log_b (PQ), the Power Property states that n⋅log⁡b(P)=log⁡b(Pn)n \cdot \log_b (P) = \log_b (P^n), and the Quotient Property states that log⁡b(P)−log⁡b(Q)=log⁡b(PQ)\log_b (P) - \log_b (Q) = \log_b \left(\frac{P}{Q}\right).
  3. Match equation with property: Match the given equation with the correct property.\newlineThe given equation is log⁡33+log⁡36=log⁡318\log_3 3 + \log_3 6 = \log_3 18. This matches the form of the Product Property, which states that the sum of the logarithms is equal to the logarithm of the product of the bases: log⁡b(P)+log⁡b(Q)=log⁡b(PQ)\log_b (P) + \log_b (Q) = \log_b (PQ).
  4. Verify equation using property: Verify the equation using the Product Property.\newlineUsing the Product Property, we can combine the logarithms on the left side of the equation: log⁡3(3×6)=log⁡318\log_3 (3 \times 6) = \log_3 18. Since 3×63 \times 6 equals 1818, the equation is correct and demonstrates the Product Property.

More problems from Identify properties of logarithms

Question
Write the exponential equation in logarithmic form.\newline93=7299^3 = 729\newlinelog⁡□729=3\log_\square 729 = 3
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the exponential equation in logarithmic form.\newlinee4≈54.598e^4 \approx 54.598\newlineln⁡____≈4\ln\_\_\_\_ \approx 4
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the logarithmic equation in exponential form.\newlinelog⁡10100=2\log_{10}100 = 2\newline102=‾10^2 = \underline{\hspace{2em}}
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.\newlineln⁡(e)10=\frac{\ln (e)}{10} = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Rewrite as a quotient of two common logarithms. Write your answer in simplest form.\newlinelog⁡333=\log_3 33 = ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate. Round your answer to the nearest thousandth.\newlinelog⁡550=\log_{5}50 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Expand the logarithm. Assume all expressions exist and are well-defined.\newlineWrite your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.\newlinelog⁡(uv)\log(uv)\newline_____
Get tutor helpright-arrow

Posted 2 months ago

Question
Expand the logarithm. Assume all expressions exist and are well-defined.\newlineWrite your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.\newlinelog⁡v7\log v^7 \newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Expand the logarithm. Assume all expressions exist and are well-defined.\newlineWrite your answer as a sum or difference of base-66 logarithms or multiples of base-66 logarithms. The inside of each logarithm must be a distinct constant or variable.\newlinelog⁡6w6\log_6 w^6\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
56x856x8
Get tutor helpright-arrow

Posted 8 hours ago

View all (19)