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 log equation as an exponential equation. You do not need to solve for x. log_(4x)(2x-7)=3x-5 Answer:

Write the log equation as an exponential equation. You do not need to solve for x \mathrm{x} .\newlinelog⁡4x(2x−7)=3x−5 \log _{4 x}(2 x-7)=3 x-5 \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Change of base formularight chevron icon

Full solution

Q. Write the log equation as an exponential equation. You do not need to solve for x \mathrm{x} .\newlinelog⁡4x(2x−7)=3x−5 \log _{4 x}(2 x-7)=3 x-5 \newlineAnswer:
  1. Rewrite as Exponential Equation: The logarithmic equation log⁡4x(2x−7)=3x−5\log_{4x}(2x-7)=3x-5 can be rewritten as an exponential equation by using the definition of a logarithm. The definition states that if log⁡a(b)=c\log_{a}(b)=c, then ac=ba^{c}=b. Here, aa is the base of the logarithm, bb is the argument, and cc is the logarithm's value.
  2. Use Logarithm Definition: Using the definition, we can rewrite log⁡4x(2x−7)=3x−5\log_{4x}(2x-7)=3x-5 as (4x)3x−5=2x−7(4x)^{3x-5}=2x-7. This is because the base is 4x4x, the argument is 2x−72x-7, and the value of the logarithm is 3x−53x-5.

More problems from Change of base formula

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

Posted 3 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 3 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 3 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 3 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 3 months ago

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

Posted 3 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 3 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 3 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 3 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 3 months ago

View all (16)