Asked by heather

Given that x=logbase3 5 and
y=logbase3 2 , rewrite logbase3 60 in terms of x and y.
Answered by Reiny
given:
x = log<sub>3</sub> 5 ----> 3^x = 5
y = log<sub>3</sub> 2 ----> 3^y = 2

let log<sub>3</sub> 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
log<sub>3</sub>60 = x+2y+1
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