Given that x=logbase3 5 and

Question

y=logbase3 2 , rewrite logbase3 60 in terms of x and y.

Answer 1

given:
x = log₃ 5 ----> 3^x = 5
y = log₃ 2 ----> 3^y = 2

let log₃ 60 = z ---- 3^z = 60

3^z = 60
= (3)(2)(2)(5)
= (3^0)(3^y)(3^y)(3^x)
= 3(1+y+y+x)
= 3^(x+2y+1)

then z = x+2y+1
log₃60 = x+2y+1