logs problem? if 5^x = 3....?
If 5^x = 3 and 5^y = 4 express in terms of x and y: log(base 5)0.75
im not even sure where to start with this problem. any help would be appreciated. :)
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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)