f4 maths

the first question

log(100y)
-----------------
1+log(y^1/2)

log(100y)
=------------------------ ( i.e. log10 =1)
log10+log(y^1/2)

log(100y)
=------------------------ (as logA+logB=logAB i.e. log10+logy^1/2=log10y^1/2)
log(10y^1/2)

log(10y^1/2 * 10y^1/2)
=-----------------------------------
log(10y^1/2)

log(10y^1/2)+log(10y^1/2)
=----------------------------------------- (because logAA=logA+logA=2logA)
log(10y^1/2)

2log(10y^1/2)
=--------------------------
log(10y^1/2)

= 2

so the answer is 2


for question 2
the answer is really a+b

no 1 , the Question is not clear.
no2,
(a^3 +b^3) / (a^2 - ab + b^2)
= (a +b)(a^2 - ab + b^2) / (a^2 - ab + b^2)
= a +b