The value of `lim_(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x)` is ________.A. 3B. 1C. `(2)/(3)`D. `(3)/(2)`

The value of `lim_(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x)` is ________

1.	The value of `lim_(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x)` is ________.A. 3B. 1C. `(2)/(3)`D. `(3)/(2)`
Answer» Correct Answer - `(4)` We have, `y=underset(xtooo)lim((20^(x)-1)/(19(5^(x))))^((1)/(x))" "(oo^(0)" form")` `:." "log_(e)y=log_(e)underset(xtooo)lim((20^(x)-1)/(19(5^(x))))^((1)/(x))` `=underset(xtooo)limlog_(e)((20^(x)-1)/(19(5^(x))))^((1)/(x))` `=underset(xtooo)lim(1)/(x)log_(e)((20^(x)-1)/(19(5^(x))))` `=underset(xtooo)lim(log_(e)(20^(x)-1)-log_(e)19-log_(e)5^(x))/(x)` `=underset(xtooo)lim((20^(x)xxlog_(e)20)/(20^(x)-1)-0-(5^(x)log_(e)5)/(5^(x)))/(1)` `=underset(xtooo)lim(((log_(e)20)/(1))/(1-(1)/(20^(x)))-log_(e)5)` `=log_(e)20-log_(e)5=log_(e)4`

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