the value of log √(a√(a√(a√a))) to the base a^(1/4) where a>0, a not =0 is

Asked by sibaprasad1972 | 28th Jul, 2019, 11:41: PM

Expert Answer:

begin mathsize 16px style log subscript straight a to the power of 1 fourth end exponent end subscript space open parentheses square root of left parenthesis straight a square root of straight a square root of straight a square root of straight a end root end root end root close parentheses end style
begin mathsize 16px style equals log subscript straight a to the power of 1 fourth end exponent space space end subscript square root of straight a square root of straight a square root of straight a to the power of 3 over 2 end exponent end root end root end root end style
begin mathsize 16px style equals log subscript straight a to the power of 1 fourth end exponent space space end subscript square root of straight a square root of aa to the power of 3 over 4 end exponent end root end root end style
begin mathsize 16px style equals log subscript straight a to the power of 1 fourth end exponent space space end subscript square root of straight a square root of straight a to the power of 7 over 4 end exponent end root end root end style
begin mathsize 16px style equals log subscript straight a to the power of 1 fourth end exponent space space end subscript square root of aa to the power of 7 over 8 end exponent end root end style
begin mathsize 16px style equals log subscript straight a to the power of 1 fourth end exponent space space end subscript square root of straight a to the power of 15 over 8 end exponent end root end style
begin mathsize 16px style equals log subscript straight a to the power of 1 fourth end exponent space space end subscript straight a to the power of 15 over 16 end exponent end style
begin mathsize 16px style equals log subscript straight a to the power of 1 fourth end exponent space space end subscript straight a to the power of 1 fourth cross times 15 over 4 end exponent end style
Error converting from MathML to accessible text.
= 15/4                  

Answered by Sneha shidid | 29th Jul, 2019, 10:10: AM