If a^b = c, then log(base a)(c) = b. It becomes a question - to what power bust we raise a to get c?
In this case a = 8, b = (1/3), c = 2. Therefore:
log(base 8)(2) = (1/3)
I hope this helps :)
Answer:
The Answer is D.
Step-by-step explanation:
To solve this question we should use the process of elimination.
We can clearly see that the function f(x) increases as x increases so we can rule out options A and C.
Now we have to decide between B and D.
So the format for a quadratic function is 
The format for an exponential function is 
So let's try exponential first:
at x = 0 we solve for a and b:
so we find b when x =5
![12201.9 =10000b^5\\b^5=\frac{12201.9}{10000} \\b^5=1.22019\\b=\sqrt[5]{1.22019} \\](https://tex.z-dn.net/?f=12201.9%20%3D10000b%5E5%5C%5Cb%5E5%3D%5Cfrac%7B12201.9%7D%7B10000%7D%20%5C%5Cb%5E5%3D1.22019%5C%5Cb%3D%5Csqrt%5B5%5D%7B1.22019%7D%20%5C%5C)
b = 1.04060
Then we evaluate the value as x=10
![14888.64=10000b^10\\b^10=14888.64/10000\\b^10=1.488864\\b=\sqrt[10]{1.488864} \\b=1.04060](https://tex.z-dn.net/?f=14888.64%3D10000b%5E10%5C%5Cb%5E10%3D14888.64%2F10000%5C%5Cb%5E10%3D1.488864%5C%5Cb%3D%5Csqrt%5B10%5D%7B1.488864%7D%20%5C%5Cb%3D1.04060)
As can be seen from both cases b is the same. This is a key chareteristic of an exponential function. So the Answer is D.
Answer: x=10
Step-by-step explanation:
3x+2/24=12/9
9(3x+2)=288
27×+18=288
-18
27x=270/27
x=10
Answer:
Only whole numbers of people, n, are assumed in the calculation.
Step-by-step explanation:
The function relating the number of people, n, to the revenue, r, implicity assumes that only whole people will purchase tickets. 13.5 would mean that 13 normal people and 1/2 of a person bought tickets. This can't be in the domain, since the ticket saleperson would run away if 1/2 of a person showed up: thus no ticket sale.
Actually, it may depend on how one defines a person. Is it 1/2 physically, or 1/2 mentally? I've personally seen the latter show up at some fundraisers.
Answer:
x-intercepts are (0, 0) and (-6, 0)
Step-by-step explanation:
equation of a parabola in vertex form: y = a(x - h)² + k
where (h, k) is the vertex
Substituting the given vertex (-3, -18) into the equation:
y = a(x + 3)² - 18
If the y-intercept is (0, 0) then substitute x=0 and y=0 into the equation and solve for a:
0 = a(0 + 3)² - 18
⇒ 0 = a(3)² - 18
⇒ 0 = 9a - 18
⇒ 9a = 18
⇒ a = 2
Therefore, y = 2(x + 3)² - 18
To find the x-intercepts, set the equation to 0 and solve for x:
2(x + 3)² - 18 = 0
Add 18 to both sides: 2(x + 3)² = 18
Divide both sides by 2: (x + 3)² = 9
Square root both sides: x + 3 = ±3
Subtract 3 from both sides: x = ±3 - 3
so x = 3 - 3 = 0
and x = -3 - 3 = -6
So x-intercepts are (0, 0) and (-6, 0)
