Given that $ 7 7 7 7 7 = 117649^a $ Then find the value of a.

Given that $ 7 7 7 7 7 = 117649^a $ The… | Answer

Subject

Quantitative Aptitude

Topic

Simplification

Given that $\sqrt {7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \ldots \ldots \ldots } } } } } = {117649^a}$ Then find the value of a.
Reading

ক)

1/2

খ)

1/3

গ)

1/4

ঘ)

1/5

ঙ)

None of these

Explanation

Laws of indices: (a m ) n = a m × n a m × a n = a m+n a m ÷ a n = a m-n LHS =

\sqrt {7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \ldots \ldots \ldots } } } } }

and RHS = 117649a Let LHS = y, then

y = \sqrt {7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \ldots \ldots \ldots } } } } } \;

Or y = √(7y) Squaring both sides, we get ⇒ y 2 = 7y ⇒ y 2 – 7y = 0 ⇒ y (y – 7) = 0 Since y is a non-zero number, thus y = 7 Now, RHS = 7 Or, 117649 a = 7 ⇒ (7 6 ) a = 7 ⇒ 7 6a = 7 Comparing both sides, we obtain 6a = 1 Or, a = 1/6

The difference of 1 (3/16) and its reciprocal is equal to What should come in place of question mark (?) in the following question? (43% of 2750) – (38% of 2990) =?How many (1/8)s are there in 37 (1/2)?If

x = \sqrt {\left( {1.96} \right)} - \sqrt {\left( {0.04} \right)}

then the value of x is Find the value -2+(-2)-{-(2)}-2 Let a = (4 ÷ 3) ÷ 3 ÷ 4, b = 4 ÷ (3 ÷ 3) ÷ 4, c = 4 ÷ 3 ÷ (3 ÷ 4). The maximum value among the above three is What will come in place of the question mark (?) in the following equation? 160 km 80 m ÷ 6 = ?If I = (3/4) ÷ (5/6), II = 3 ÷ [(4 ÷ 5) ÷ 6], III = [3 ÷ (4 ÷ 5)] ÷ 6, IV = 3 ÷ 4 ÷ (5 ÷ 6), then

Given that 77777……………=117649a\sqrt {7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \ldots \ldots \ldots } } } } } = {117649^a}77777……………​​​​​=117649a Then find the value of a.Reading

Given that 77777……………=117649a\sqrt {7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \ldots \ldots \ldots } } } } } = {117649^a}77777……………​​​​​=117649a Then find the value of a.

Explanation

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Given that $\sqrt {7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \ldots \ldots \ldots } } } } } = {117649^a}$ Then find the value of a.
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Given that $\sqrt {7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \ldots \ldots \ldots } } } } } = {117649^a}$ Then find the value of a.