What is the value of x satisfying the equation \(\frac{4^{2x}}{4^{3x}}\) = 2?
-2
-\(\frac{1}{2}\)
\(\frac{1}{2}\)
2
Correct answer is B
\(\frac{4^{2x}}{4^{3x}}\) = 2
42x - 3x = 2
4-x = 2
(22)-x
= 21
Equating coefficients: -2x = 1
x = -\(\frac{1}{2}\)
Evaluate \(\log_{b} a^{n}\) if \(b = a^{\frac{1}{n}}\).
n2
n
\(\frac{1}{n}\)
\(\frac{1}{n^2}\)
Correct answer is A
Let \(\log_{b} a^{n} = x\)
\(\therefore a^{n} = b^{x}\)
\(a^{n} = (a^{\frac{1}{n}})^{x}\)
\(a^{n} = a^{\frac{x}{n}} \implies n = \frac{x}{n}\)
\(x = n^{2}\)
\(\frac{1}{25}\)
\(\frac{1}{4}\)
4
25
Correct answer is C
% error in Area = \(\frac{\pi(5.1)^2 - \pi(5)^2 \times 100%}{\pi(5)^2}\)
= \(\frac{\pi 26.01 - 25 \times 100%}{\pi(25)}\)
= \(\frac{1.01}{25}\) x 100%
= 4.04%
5
6
7
8
Correct answer is A
To find n if 34n = 100112, convert both sides to base 10
= 3n + 4 = (1 x 24) + (0 x23) + (0 x 22) + (1 x 21) + 1 x 2o
= 3n + 4 = 16 + 0 + 0 + 2 + 1
3n + 4 = 19
3n = 15
n = 5
\(\frac{1}{8}\)
\(\frac{1}{24}\)
\(\frac{1}{12}\)
\(\frac{1}{4}\)
Correct answer is C
Chance of x = \(\frac{1}{2}\)
Change of Y = \(\frac{2}{3}\)
Chance of Z = \(\frac{1}{4}\)
Chance of Y and Z only occurring
= Pr (Y ∩ Z ∩ Xc)
where Xc = 1 - Pr(X)
1 - \(\frac{1}{2}\) = \(\frac{1}{2}\)
= Pr(Y) x Pr(Z) x Pr(Xc)
= \(\frac{2}{3}\) x \(\frac{1}{4}\) x \(\frac{1}{2}\)
= \(\frac{1}{12}\)