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:

Write the expression below as a single logarithm in simplest form. 2log_(b)3+log_(b)6 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline2log⁡b3+log⁡b6 2 \log _{b} 3+\log _{b} 6 \newlineAnswer: log⁡b(□) \log _{b}(\square)

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

Full solution

Q. Write the expression below as a single logarithm in simplest form.\newline2log⁡b3+log⁡b6 2 \log _{b} 3+\log _{b} 6 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Identify Properties: Identify the properties used to combine logarithms.\newlineThe expression 2log⁡b3+log⁡b62\log_{b}3 + \log_{b}6 involves two logarithmic terms that can be combined using the power property and the product property of logarithms.\newlinePower Property: log⁡b(Pk)=k⋅log⁡bP\log_b (P^k) = k \cdot \log_b P\newlineProduct Property: log⁡bP+log⁡bQ=log⁡b(P⋅Q)\log_b P + \log_b Q = \log_b (P \cdot Q)
  2. Apply Power Property: Apply the power property to the first term.\newlineThe power property allows us to move the coefficient of the logarithm inside as an exponent of the argument.\newline2log⁡b3=log⁡b(32)2\log_{b}3 = \log_{b}(3^2)
  3. Simplify Exponent: Simplify the exponent.\newlineCalculate the value of 323^2.\newline32=93^2 = 9\newlineSo, 2log⁡b32\log_{b}3 becomes log⁡b9\log_{b}9.
  4. Apply Product Property: Apply the product property to combine the logarithms.\newlineNow, we can use the product property to combine log⁡b9\log_{b}9 and log⁡b6\log_{b}6 into a single logarithm.\newlinelog⁡b9+log⁡b6=log⁡b(9×6)\log_{b}9 + \log_{b}6 = \log_{b}(9 \times 6)
  5. Calculate Product: Calculate the product inside the logarithm.\newlineMultiply 99 by 66 to get the argument of the combined logarithm.\newline9×6=549 \times 6 = 54\newlineSo, log⁡b9+log⁡b6\log_{b}9 + \log_{b}6 becomes log⁡b54\log_{b}54.
  6. Write Final Answer: Write the final answer.\newlineThe expression 2log⁡b3+log⁡b62\log_{b}3 + \log_{b}6 as a single logarithm in simplest form is:\newlinelog⁡b54\log_{b}54

More problems from Quotient property 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
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}
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

View all (60)