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. Write your answer as an integer or a fraction in simplest form. \newline16=2x16 = 2^x \newlinex=x = ______

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve exponential equations by rewriting the baseright chevron icon

Full solution

Q. Solve. Write your answer as an integer or a fraction in simplest form. \newline16=2x16 = 2^x \newlinex=x = ______
  1. Rewrite as Power of 22: Rewrite 1616 as a power of 22. 1616 is 22 raised to the power of 44, because 2×2×2×22 \times 2 \times 2 \times 2 equals 1616. So, 16=2416 = 2^4.
  2. Set Exponents Equal: Set the exponents equal to each other since the bases are the same.\newline2x=242^x = 2^4\newlineTherefore, x=4x = 4.

More problems from Solve exponential equations by rewriting the base

Question
Solve. Write your answer as an integer or a fraction in simplest form.\newline5x=15^x=1\newlinex=x= _____
Get tutor helpright-arrow

Posted 3 months ago

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

Posted 3 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 \newlinef(1)= f(1) = _____
Get tutor helpright-arrow

Posted 2 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 2 months ago

Question
Solve. Round your answer to the nearest thousandth.\newline7=9x7 = 9^x\newlinex=x = ____
Get tutor helpright-arrow

Posted 3 months ago

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

Posted 2 months ago

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

Posted 3 months ago

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

Posted 2 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 3 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) = 6^x\newline(B) f(x)=6xf(x) = 6x\newline(C) f(x)=16xf(x) = \frac{1}{6^x}\newline(D) f(x)=x6f(x) = \frac{x}{6}
Get tutor helpright-arrow

Posted 3 months ago

View all (84)