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)8 Answer: log_(b)(◻)

Write the expression below as a single logarithm in simplest form.\newline2log⁡b8 2 \log _{b} 8 \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⁡b8 2 \log _{b} 8 \newlineAnswer: log⁡b(□) \log _{b}(\square)
  1. Question Prompt: Question Prompt: Write the expression 2log⁡b82\log_{b}8 as a single logarithm in simplest form.
  2. Identify Property: Identify the property used to write the expression as a single logarithm.\newlineThe Power Property of logarithms states that a coefficient in front of a logarithm can be rewritten as an exponent inside the logarithm. The property is: alog⁡b(x)=log⁡b(xa)a\log_b(x) = \log_b(x^a).
  3. Apply Power Property: Apply the Power Property to the given expression.\newlineUsing the Power Property, we can rewrite 2log⁡b82\log_{b}8 as log⁡b(82)\log_{b}(8^2).
  4. Calculate Exponent: Calculate the exponent. 828^2 equals 6464.
  5. Write Final Expression: Write the final expression.\newlineThe expression 2log⁡b82\log_{b}8 can be written as log⁡b(64)\log_{b}(64).

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)