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T h e space v a l u e space o f space 0.2 to the power of log subscript square root of 5 end subscript open parentheses 1 fourth plus 1 over 8 plus 1 over 16 plus... close parentheses end exponent space i s

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Asked by Topperlearning User 7th October 2016, 4:00 PM
Answered by Expert
Answer:

1 fourth plus 1 over 8 plus 1 over 16 plus.... equals fraction numerator begin display style 1 fourth end style over denominator 1 minus begin display style 1 half end style end fraction equals 1 half
T equals log subscript square root of 5 end subscript 1 half equals fraction numerator log begin display style 1 half end style over denominator log square root of 5 end fraction equals fraction numerator negative log 2 over denominator begin display style 1 half end style log 5 end fraction equals fraction numerator negative 2 log 2 over denominator log 5 end fraction equals log subscript 5 1 fourth space space space space space space space space open square brackets U sin g space t h e space p r o p e r t y space log subscript a b equals fraction numerator log b over denominator log a end fraction space a n d space log a to the power of n equals n log a close square brackets space
0.2 equals 1 fifth
0.2 to the power of T equals 1 over 5 to the power of T equals 1 over 5 to the power of log subscript 5 begin display style 1 fourth end style end exponent equals fraction numerator 1 over denominator begin display style 1 fourth end style end fraction equals 4 space space space space open square brackets x to the power of log subscript x a end exponent equals a close square brackets

Answered by Expert 7th October 2016, 6:00 PM
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