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Latest gcse maths notes at astarmathsandphysics.com

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astarmathsandphysics:
Finding
the Mean of a Frequency TableFinding
the Highest Common Factor (HCF) of Two NumbersMode,
Median and MeanStandard
FormPercentages,
Fractions and DecimalsFinding
the Lowest Common Multiple of Two Numbers

sweetest angel:
hey,Thanks for the links but i have a problem in logs that i'll be very grateful if u solve
i'll use ^ to indicat a number power
Q: prove that if a^x=b^y=(ab)^xy, then x+y=1
this is a question from C2 AS edexcel. thanks a lot in advance  :D

astarmathsandphysics:
a^x=b^y=(ab)^xy, then x+y=1
a^x=a^(xy)b^(xy) take the xth root to get a=a^yb^y (1)
and the the yth root of b^y=a^(xy)b^(xy) to get b=a^xb^x (2)
a^(1-y)=b^y from (1) and b=a^(1-y)/y from (1)
sub into (2) to get a^(1-y)/y=a^xa^x(1-y)/y
hence (1-y)/y=x+x(1-y)/y
1-y=xy+x-xy so 1=x+y

tricky question

astarmathsandphysics:
definitely in the wrong topic too.

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