make x the subjectWatch
To make x the subject, you need to 'move' the -5 from the right hand side of the equation onto the left hand side.
We do this by adding 5 to both sides. This is because -5 + 5 = 0 and so we will simply be left with: y + 5 = x + 0 which is the same as y+5 = x. This is the right answer, but we usually prefer to write it as x = y+5.
Now try making x the subject of the following:
(1) y = x + 2
(2) y = 2 - x
(3) 2y + 3 = 2x -1
Now we have to make X, the subject
If something is divided by another thing and you wish to make the whatever is on the top the subject, in this case X. You simply multiply the bottom to each side of the question.
X =(A^2) (3B) (2C)
That's how you do it.
-multiply both sides by 2
-now take square roots of both sides
Sqrt(2y) = sqrt(2x) - sqrt(10)
-rewrite everything in terms of powers
2y^(1/2) = 2x^(1/2) - 10^(1/2)
Now the problem is you've got powers to deal with so best thing here is to take logs of both sides.
log 2y^(1/2) = log 2x^(1/2) - log 10^(1/2)
now you can use the logarithmic power rule logb(x y) = y ∙ logb(x)
So this becomes: 1/2 * log 2y = 1/2 * log 2x -1/2 * log 10
let's rearrange and factorize:
1/2 * log 2y - 1/2 * log 2x = -1/2 log 10
1/2 (log 2y - log 2x)= -1/2 log 10 Divide both sides by 1/2
log(2y -2x) = -1
now you have to find a way to remove logs from both sides otherwise we can not change subject right? so because we need same base which is log, so they cancel out !
you have to rewrite -1 as logs so we have logs on both sides. i didn't write before but all logs here were base 10
so -1 in log 10 base is log (10) (10^-1)
so this becomes
Log(10)(2y-2x) = -1 log (10)
Use logarithmic power rule again to bring -1 as power
Log (10)(2y-2x)= log(10)^1
now logs cancel out and you're left with
2y -2x = 10
You can not make x subject till x is not alone in one side so lets first rearrange:
2x = 2y -10
and now divide both sides by 2.
x = 5 - y
It's actually quite simple but you need to remember logs and their properties.