A student attempts to prove that loga(x+y)=logax+logay\log_a(x+y)=\log_a x+\log_a yloga(x+y)=logax+logay as follows.
"Let x=apx=a^px=ap and y=aqy=a^qy=aq. Then x+y=ap+aq=ap+qx+y=a^p+a^q=a^{p+q}x+y=ap+aq=ap+q."
Identify the incorrect step.
Give values of aaa, x x\,x and y y\,y that disprove the claimed law.
8 exam-style questions on WJEC A Level Maths 1.1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.