This is for math homework. I need to find an exact solution and then (if possible) use a calculator to find a numerical approximation to the solution.
Can an exponent be a fraction?
2006-07-24 15:41:58 · 13 answers · asked by studentsmom 1 in Science & Mathematics ➔ Mathematics
3 * 2^x + 8 = 25
3 * 2^x = 17
2^x = 17/3
log (2^x) = log (17/3)
x log 2 = log (17/3)
x = log (17/3) / log 2
x = 2.50...
2006-07-24 15:51:37 · answer #1 · answered by Anonymous · 2⤊ 0⤋
Yes an exponent can be a fraction. It is called a Rational Exponent. These sort of exponents occur in compound interest applications.
Solution: 3 * 2^x + 8 = 25
Subtract 8 from both sides: 3 * 2^x = 17
Divide both sides by 3: 2^x = (17/3)
Take the Log(base 2) of both sides:
Log(base 2) [2^x] = Log(base 2) [17/3]
By the Inverse Function Theorem: x = Log(base 2) [17/3]
This is a valid answer simce 17/3 is in the Domain of Log(base 2)
It is the so called "exact answer".
The problem is that your calculator may not have base 2 log capability. In this case convert the answer into Base 10 (common) log using the change of base formula as follows:
Log(base 2) [17/3] = Log [17/3] / Log[2]
Here "Log" means base 10 which is one of your calculator keys.
Hope that helps !
2006-07-24 15:55:41 · answer #2 · answered by mathguy 2 · 0⤊ 0⤋
3x - 5y = 20 6x + 5y = 25 Use the addition approach to characteristic a similar words in each and each equation. This removes the y term so which you will resolve for x: 3x - 5y = 20 6x + 5y = 25 ------------------- 9x + 0 = 40 5 9x = 40 5 x = 40 5/9 x = 5 Now replace x = 5 into the two of the equations to locate y: 6(5) + 5y = 25 30 + 5y = 25 5y = 25 - 30 5y = -5 y = -5/5 y = -a million the respond is x = 5, y = -a million
2016-11-02 22:40:07 · answer #3 · answered by shuman 3 · 0⤊ 0⤋
My understanding is that the problem is 3*(2^x) + 8 =25. If so, then 3*(2^x)=17 then 2^x=17/3 then log(2^x)=log(17/3) then x* log(2) = log (17/3) then x= (log(17/3))/log(2).
2006-07-24 15:49:57 · answer #4 · answered by ConradD 2 · 0⤊ 0⤋
3 * 2^x + 8= 25 ==> 3 * 2^x = 17 ==> 2^x = 17/3 ==> solve by log
log (2^x) = log (17/3) => x log 2 = log (17/3) => x = (log 17/3) / (log 2)
2006-07-24 15:47:48 · answer #5 · answered by ___ 4 · 0⤊ 0⤋
3 * 2^x + 8 = 25
3 * 2^x = 17
2^x = 17/3
log(base2)(2^x) = x = log(base2)(17/3) = ln (17/3) / ln 2
x = 2.5025003405291832268003270668626
That's what my Window calculator gives me. Hope that helps.
2006-07-24 15:51:55 · answer #6 · answered by Ѕємι~Мαđ ŠçїєŋŧιѕТ 6 · 0⤊ 0⤋
2 ** x = 17/3
x = log(base2) (17/3)
exponent can b irrational or even complex also what about fraction
2006-07-24 15:45:10 · answer #7 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
2.50. And yes an exponent can be a fraction.
2006-07-24 15:46:42 · answer #8 · answered by thedecider20 2 · 0⤊ 0⤋
Somewhere between 2.1 and 2.5. I don't feel like getting out a calculator.
2006-07-24 15:46:07 · answer #9 · answered by CStoos 2 · 0⤊ 0⤋
x=1.581, but not sure about this one...
yes, a fraction can be an exponent...
2006-07-24 15:47:17 · answer #10 · answered by cooldude 5 · 0⤊ 0⤋