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 3ln 3-ln 5 as a single logarithm in simplest form without any negative exponents. Answer: ln(◻)

Write the expression 3ln⁡3−ln⁡5 3 \ln 3-\ln 5 as a single logarithm in simplest form without any negative exponents.\newlineAnswer: ln⁡(□) \ln (\square)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Change of base formularight chevron icon

Full solution

Q. Write the expression 3ln⁡3−ln⁡5 3 \ln 3-\ln 5 as a single logarithm in simplest form without any negative exponents.\newlineAnswer: ln⁡(□) \ln (\square)
  1. Apply power rule: Apply the power rule of logarithms to the term 3ln⁡33\ln 3. The power rule states that a⋅log⁡b(c)=log⁡b(ca)a \cdot \log_b(c) = \log_b(c^a). Therefore, 3ln⁡33\ln 3 can be rewritten as ln⁡(33)\ln(3^3). Calculation: ln⁡(33)=ln⁡(27)\ln(3^3) = \ln(27).
  2. Combine logarithmic terms: Combine the two logarithmic terms using the quotient rule.\newlineThe quotient rule states that log⁡b(m)−log⁡b(n)=log⁡b(mn)\log_b(m) - \log_b(n) = \log_b\left(\frac{m}{n}\right).\newlineTherefore, ln⁡(27)−ln⁡(5)\ln(27) - \ln(5) can be combined into a single logarithm as ln⁡(275)\ln\left(\frac{27}{5}\right).\newlineCalculation: ln⁡(27)−ln⁡(5)=ln⁡(275)\ln(27) - \ln(5) = \ln\left(\frac{27}{5}\right).

More problems from Change of base formula

Question
Solve for xx.\newline5x=15^x=1\newline\newlineWrite your answer in simplest form.
Get tutor helpright-arrow

Posted 5 months ago

Question
Steven opened a savings account and deposited $100.00\$100.00 as principal. The account earns 9%9\% interest, compounded annually. What is the balance after 55 years?\newlineUse the formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}, where AA is the balance (final amount), PP is the principal (starting amount), rr is the interest rate expressed as a decimal, nn is the number of times per year that the interest is compounded, and tt is the time in years.\newlineRound your answer to the nearest cent.
Get tutor helpright-arrow

Posted 4 months ago

Question
Use the following function rule to find f(1) f(1) .\newlinef(x)=12(7)x+8 f(x) = 12(7)^x + 8
Get tutor helpright-arrow

Posted 5 months ago

Question
The town of Valley View conducted a census this year, which showed that it has a population of 1,8001,800 people. Based on the census data, it is estimated that the population of Valley View will grow by 12%12\% each decade.\newlineWrite an exponential equation in the form y=a(b)xy = a(b)^x that can model the town population, yy, xx decades after this census was taken.\newlineUse whole numbers, decimals, or simplified fractions for the values of aa and bb.\newliney=y = ______
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for xx. \newline7=9x7 = 9^x\newlineRound your answer to the nearest thousandth.
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve. Round your answer to the nearest thousandth.\newline7=ex7 = e^x\newlinex=x = ____
Get tutor helpright-arrow

Posted 7 months ago

Question
Solve. Simplify your answer.\newlinelog⁡u=1\log u = 1\newlineu=u = ____
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve. Simplify your answer.\newline7log⁡x=77\log x = 7\newlinex=x = ____
Get tutor helpright-arrow

Posted 7 months ago

Question
How does g(t)=3t g(t) = 3^t change over the interval from t=3 t = 3 to t=4 t = 4 ?\newlineChoices:\newline(A) g(t) g(t) decreases by 3 3 \newline(B) g(t) g(t) increases by 3 3 \newline(C) g(t) g(t) decreases by 3% 3\%\newline(D) g(t) g(t) increases by 200%200\%
Get tutor helpright-arrow

Posted 4 months ago

Question
A function f(x) f(x) increases by 6 6 over every unit interval in x x and f(0)=0 f(0) = 0 .\newlineWhich could be a function rule for f(x) f(x) ?\newlineChoices:\newline(A) f(x)=6xf(x) = 6x\newline(B) f(x)=6xf(x) = 6^x\newline(C) f(x)=16xf(x) = \frac{1}{6^x}\newline(D) f(x)=x6f(x) = \frac{x}{6}
Get tutor helpright-arrow

Posted 4 months ago

View all (15)

Related topics

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