G C S E Find Y Without The Use Of A Calculator Or Tables

[kuiperbelt]

Please see link below:

https://ibb.co/dBQ67m3

[roslyn251254]

change the 9 and the 27 to powers of 3 then you can work with them

[roslyn251254]

...and the 243 ...

[JJ109]

243 = 9^0.75 * 27^y
Rewrite to base 3
3^5 = (3^2)^0.75 * (3^3)^Y
3^5 = 3^1.5 * 3^3y
5 = 1.5 + 3y
3.5 = 3y
y = 3.5/3

[Etch]

Yes, y = 7/6
The relationships to use are:
(X^m)^n = X^(m.n)
X^m . X^n = X^(m+n)
where '^' represents exponentiation ("to the power of")

[bobbinwales]

^ and where '.' means 'x' ('multiplied by')....and I learnt a new word- exponentiation

[Old_Geezer]

I like to think I'm reasonably intelligent but this would have had me foxed completely. I guess if you are taught a particular maths syllabus then you will know; but I was all at sea with it I'm going to reread the answers though and learn something.