1

log5 base3 = x and log11 base25=y then value of log(11÷3) base3 in terms of x and y is ?

0

Using the basic log properties like:

- log
_{b}(x/y) = log_{b}(x) - log_{b}(y) - log
_{b}(x^{y}) = y * log_{b}(x) - log
_{b}(x) = log_{c}(x) / log_{c}(b) - log
_{b}(b) = 1 - log
_{b}(c) = 1 / log_{c}(b) - log
_{bp}(x) = (1/p) * log_{b}(x) ---> (base was in power p)

=> Given

log_{3}(5) = x

=> log_{5}(3) = 1/x -------(property (5)

and

log_{25}(11) = y

= log_{52}(11) = y

= (1/2) * log_{5}(11) = y -------(property (6)

= log_{5}(11) = 2y

To find:

log_{3}(11/3)

= log_{3}(11) - log_{3}(3) ------(using property (1)

= log_{3}(11) - 1 --------(property (4))

= [ log_{5}(11) / log_{5}(3) ] -1 ---------(property (3)

= 2xy -1