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◇◇Content Quality Required◇◇The value of is :(a) 1(b) 3(c) 4(d) None of these.I need well explained answer.

Answer»

Before solving this question , you have to be ACQUAINTED with certain identities:
These are basic formulas

a^ [log b (base a)]=b….(1)

a^ [log b (base a^n)]=b^(1/n)……..(2)

sum of infinite G.P, = a/(1-r) …(3)

Solving the exponent PART: ⅓ +(⅓)²+..............(⅓)^∞ = (⅓)/ [1-⅓ ] =½…USING(3)

0.16= 4/25

2.5=5/2

(4/25) ^ log_(5/2) [ 1/2]

(4/25) ^ log_[(4/25)^(-1/2)] [ 1/2]

Here [(4/25)^(-1/2) is the base =5/2

(4/25) ^ log_[(4/25)] [ 1/2]^(-2) …… using(2) and (1)

= 4

hope this HELPS you


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