Verified answer

log(base5) 5^x = log(base5)3

x = log(base5)3

log(base5)5^y = log(base5)4

y = log(base5)4

log(base5)0.75

=log(base5)(3/4)

=log(base5)(3) - log(base5)(4)

= x - y

If 5^x = 3 and 5^y = 4 express in terms of x and y:

log(base 5)0.75 = x -- y

5^x = 3 and 5^y = 4 express in terms of x and y: log(base 5)0.75

5^x = 3

x = log_base5(3)

5^y = 4

y = log_base 5(4)

log(base 5)0.75 = log(base 5)(3/4)

= log(base 5)(3) - log(base 5)(4)

= x - y

5^x/5^y = 3/4 OR 5^(x - y) = 3/4 = 0.75 take logarithm on both sides (x - y) = log(Base5) 0.75.

take the logs of both sides:

log(5^x) = xlog(5) = log(3)

log(5^y) = ylog(5) = log(4)

x = log(3)/log(5)

y = log(4)/log(5)