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:

a) (1)/(3)log(x)+log(3)=log(5).

a) 13log⁡(x)+log⁡(3)=log⁡(5) \frac{1}{3} \log (x)+\log (3)=\log (5) .

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. a) 13log⁡(x)+log⁡(3)=log⁡(5) \frac{1}{3} \log (x)+\log (3)=\log (5) .
  1. Combine logs using product property: Combine the logs on the left side using the product property of logarithms, which states that log⁡b(m)+log⁡b(n)=log⁡b(mn)\log_b(m) + \log_b(n) = \log_b(mn).13log⁡(x)+log⁡(3)=log⁡(313x)\frac{1}{3}\log(x) + \log(3) = \log(3^{\frac{1}{3}}x).
  2. Simplify by raising 33: Simplify the left side by raising 33 to the power of 13\frac{1}{3}.log⁡(313⋅x)=log⁡(313⋅x)\log(3^{\frac{1}{3}}\cdot x) = \log(3^{\frac{1}{3}}\cdot x).
  3. Set equal to right side: Set the simplified left side equal to the right side. log⁡(313⋅x)=log⁡(5)\log(3^{\frac{1}{3}}\cdot x) = \log(5).
  4. Arguments must be equal: Since the logs are equal, their arguments must be equal. 313⋅x=53^{\frac{1}{3}}\cdot x = 5.
  5. Solve for x: Solve for x by dividing both sides by 31/33^{1/3}. \newlinex=531/3x = \frac{5}{3^{1/3}}.

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)