Question

if log(x^2y^3)=a & log (x/y)= b ,find log x & log y in terms of a & b

Answer 1

log (x^2y^3)=a
=> logx^2 + logy^3=a
=> 2logx+ 3logy=a --------------(1)

again,
log (x/y)=b
=> logx-logy=b ----------------(2)

now ,
solve both equation (1) and (2)

hence ,
logx=(a+3b)/5
and put logx value in equation (1)
logy =(a-2b)/5