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:

Solve the equation 4×333=4x24\times3^{33}=4x^2

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Convert between exponential and logarithmic form: rational basesright chevron icon

Full solution

Q. Solve the equation 4×333=4x24\times3^{33}=4x^2
  1. Identify base and exponent: Identify the base and the exponent in the given equation. 4×333=4x24\times3^{33}=4x^2 can be simplified by dividing both sides by 44.
  2. Divide by 44: Divide both sides by 44 to simplify the equation.\newline333=x23^{33} = x^2
  3. Take square root: Take the square root of both sides to solve for xx.333=x2\sqrt{3^{33}}=\sqrt{x^2}
  4. Simplify square root: Simplify the square root of x2x^2 and the exponent.\newlinex=3332x=3^{\frac{33}{2}}

More problems from Convert between exponential and logarithmic form: rational bases

Question
Convert the exponential equation in logarithmic form.\newline93=7299^3 = 729
Get tutor helpright-arrow

Posted 6 months ago

Question
Convert the exponential equation in logarithmic form.\newlinee4≈54.598e^4 \approx 54.598
Get tutor helpright-arrow

Posted 6 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 10 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 6 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 10 months ago

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

Posted 10 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 6 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 10 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 10 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 10 months ago

View all (23)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant