How to Check Your Solutions for Equations?

[discombobulated]

Solve the equations:
a) 25^3x = 1/5^2-x
This is what I've done but i don't know if it's right so i need someone to check it for me please.
(5²)^3x = (5^-1)^2-x
6x = -2+x (x powers)
5x=-2
x= -2/5
b)3x^-1/2 - 4 = 0
errm...i'm kinda stuck on this one, could someone start me off please?
3x^-1/2 = 4
c) find the value of y
4^y+1=8^2y-1
here's what i did:
(2²)^y+1 = (2³)^2y-1
2y+2=6y-3 (powers)
4y-5=0
y=5/4
Is that right?
Thanks in advance!

 

[sanitykey]

(a) and (c) appear to be correct, as for (b)

Try and get x on it's own, i would continue by:

3x^-1/2 = 4
1/3x^1/2 = 4
12x^1/2 = 1

 

[Ouabache]

as for (b)
Try and get x on it's own, i would continue by:
3x^-1/2 = 4
1/3x^1/2 = 4
12x^1/2 = 1

you have the right concept however, something seems fishy
why did you invert 3x^-1/2? to become 1/3x^1/2?
It didn't say (3x)^-1/2 ..
I would say 3x^-1/2 = 3/(x^1/2).
Then 3/(x^(1/2)) = 4
4x^(1/2) = 3
x^(1/2) = 3/4 etc...

 

[sanitykey]

Whoops you're right Ouabache sorry about that discombobulated, my escuse is it was late when i did that reply , anyway mistake understood, i did think 1/144 was a bit of an odd answer...

 

[discombobulated]

Thanks a lot guys, i worked it out and I got the answer x= 9/16