The-value-of-a-log-b-x-where-a-0-2-b-5-x-1-4-1-8-1-16-to-is-

Question Number 56418 by gunawan last updated on 16/Mar/19

The value of a^{\log_{b} x} where a = 0.2, b = \sqrt{5,}

x = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots to \infty is

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Mar/19

x = \frac{\frac{1}{4}}{1 - \frac{1}{2}} = \frac{1}{2} = 0.5

t = {l o g}_{b} x \to b^{t} = x \to {(5)}^{\frac{t}{2}} = \frac{1}{2} = 0.5

\frac{t}{2} = {l o g}_{5} (0.5) \to t = 2 {l o g}_{5} (0.5)

s o a^{{l o g}_{b} x} \to 0 . 2^{{l o g}_{5} (0.25)}