Solve without using tables log5(62.5) - log5(\(\frac{1}{2}\))
3
4
5
8
Correct answer is A
log5(62.5) - log5(\(\frac{1}{2}\))
= log5\(\frac{(62.5)}{\frac{1}{2}}\) - log5(2 x 62.5)
= log5(125)
= log553 - 3log55
= 3
If 2log3 y + log3 x2 = 4, then y is
4 - log3
\(\frac{4}{log_3 x}\)
\(\frac{4}{x}\)
\(\pm\) \(\frac{9}{x}\)
Correct answer is D
2log3y + log3x2 = 4
log3y2 + log3x2 = 4
∴ log3 (x2y2) = log381(correct all to base 4)
x2y2 = 81
∴ xy = \(\pm\)9
∴ y = \(\pm\)\(\frac{9}{x}\)
simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
3
\(\frac{2}{3}\)
7
-4
Correct answer is D
\(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
L.C.M = (3- 2) (3 + 2)
∴ \(\frac{1}{\sqrt{3 - 2}}\) - \(\frac{1}{\sqrt{3 - 2}}\) = \(\frac{\sqrt{3 + 2} - \sqrt{3 - 2}}{\sqrt{3 - 2} + \sqrt{3 - 2}}\)
\(\frac{√3 + 2 - √3 + 2}{3 - 2√3 + 2√3 - 4}\) = \(\frac{4}{3 - 2}\)
= \(\frac{4}{-1}\)
= -4
Solve for y in the equation 10^1 x 5(2y - 2) x 4(y - 1) = 1
\(\frac{3}{4}\)
\(\frac{5}{4}\)
\(\frac{2}{3}\)
5
Correct answer is C
10y x 5(2y - 2) x 4(y - 1) = 1
but 10y - (5 x 2)y = 5y x 2y
= (Law of indices)
5y x 2y x 5(2y - 2) x 4(y - 1) = 1
but 4(y - 1) = 22(y - 1)
= 2y - 2 (Law of indices)
5y x 5(2y -2) x 2(- 2) = 1
5(3y -2) x 2y x 2(2y -2) = 1
= 5(3y -2) x 2(3y -2) = 1
But ao = 1
10(3y -2) = 10o
3y - 2 = 0
∴ y = \(\frac{2}{3}\)
If 9\(^{(x - \frac{1}{2})} = 3^{x2}\) Find x
\(\frac{1}{2}\)
1
2
3
Correct answer is B
9(x - \(\frac{1}{2}\)) 3x2 = 32(x - \(\frac{1}{2}\)) = 3x2
∴ 2(x - \(\frac{1}{2}\)) = x2
2x - 1 = x2
hence x2 - 2x + 1 = 0
(x - 1)(x - 1) = 0
x = 1