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:

What is the value of t in this equality? 0.03=3×10^(t)

What is the value of t t in this equality?\newline0.03=3×10t 0.03=3 \times 10^{t}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Convert between natural exponential and logarithmic formright chevron icon

Full solution

Q. What is the value of t t in this equality?\newline0.03=3×10t 0.03=3 \times 10^{t}
  1. Simplify left side: Now we simplify the left side of the equation.\newline0.01=10t0.01 = 10^{t}
  2. Convert to logarithmic form: Next, we convert the equation to logarithmic form to solve for tt.log⁡(0.01)=log⁡(10t)\log(0.01) = \log(10^{t})
  3. Simplify using logarithmic property: Using the property of logarithms that log⁡(bx)=xlog⁡(b)\log(b^x) = x\log(b), we can simplify the right side.\newlinelog⁡(0.01)=tlog⁡(10)\log(0.01) = t\log(10)
  4. Further simplify the equation: Since log⁡(10)\log(10) is 11, we can further simplify the equation.\newlinelog⁡(0.01)=t\log(0.01) = t
  5. Calculate log⁡(0.01)\log(0.01): Now we calculate the value of log⁡(0.01)\log(0.01).\newlinelog⁡(0.01)=−2\log(0.01) = -2
  6. Calculate tt: Finally, we have the value of tt.t=−2t = -2

More problems from Convert between natural exponential and logarithmic form

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 (13)