\(125 \times 125 \times 125 \times 125 \times 125 = 5^?\)
Answer: C
\(125 \times 125 \times 125 \times 125 \times 125 = (5^3 \times 5^3 \times 5^3 \times 5^3 \times 5^3 \times ) = 5^{(3+3+3+3+3+)} = 5^{15}\)
If \(a^x = b, b^y = c\) and \(c^z = a\), then the value of \(xyz\) is:
Answer: B
\(a^1 = c^z = (b^y)^z = b^{yz} = (a^x)^{yx} = a^{xyz}.\)
Therefore, \(xyz = 1.\)
If \(2^{(x-y)} = 8\) and \(2^{(x+y)} = 32\), then \(x\) is equal to:
Answer: C
\(2^{(x-y)} = 8 = 2^3 \)
\(\Rightarrow x-y = 3 ....(1) \)
\(2^{(x+y)} = 32 = 2^5 \)
\(\Rightarrow x+y = 5 ....(2)\)
On solving (1) & (2), we get \(x = 4.\)
If \(3^x - 3^{x-1} = 18\), then the value of \(x^x\) is:
Answer: A
\(3^x - 3^{x-1} = 18 \)
\(\Rightarrow 3^{x-1} \times (3-1) = 18 \)
\(\Rightarrow 3^{x-1} = 9 = 3^2 \)
\(\Rightarrow x-1 = 2 \)
\(\Rightarrow x = 3\).
If \(7^a = 16807\), then the value of \(7^{(a-3)}\) is:
Answer: A
\(7^a = 16807, \)
\(\Rightarrow 7^a = 7^5, a = 5\)
Therefore, \(7^{(a-3)} = 7^{(5-3)} = 7^2 = 49\)