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Mathematics
UTME / JAMB 1978
Indices, Logarithms & Surds
Solution
If (25)\(^{x - 1}\) = 64(\(\frac{5}{2}\))\(^6\), then x has the value
A
7
B
4
C
32
D
64
E
5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(25)\(^{x - 1}\) = 64(\(\frac{5}{2}\))\(^6\)
(\(\frac{5}{2}\))\(^6\) = (\(\frac{5^6}{64}\))
25\(^{x - 1}\) = 64 x (\(\frac{5^6}{64}\))
5\(^{2x - 2}\) = 5\(^6\)
2x - 2 = 6
= \(\frac{8}{2}\)
= 4
Source: Myschool Past Questions Archive (Record #32718)
Mathematics
UTME / JAMB 1978
Indices, Logarithms & Surds
Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)
A
-3
B
3
C
\(\frac{3}{5}\)
D
\(\frac{-3}{2}\)
E
1n 6 - 2 1n 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #32721)
Mathematics
UTME / JAMB 1978
Indices, Logarithms & Surds
Solution
The vectors a and b are given in terms of two perpendicular units vectors i and j on a plane by a = 2i - 3j, b = -i + 2j. Find the magnitude of the vector a + 3b
A
2
B
4
C
\(\sqrt{10}\)
D
35
E
2.2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
a = 2i - 3j - 3i + 6j
= -i + 3j
= \(\sqrt{5 \times 2}\)
= \(\sqrt{10}\)
Source: Myschool Past Questions Archive (Record #32726)