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Need help solving an equation

Solve the equation. 25^x = 5^4x+1

Can someone please help me and explain how to get to the answer? Thanks.
Reply 1
25 can be simplified into a power of 5. Make sure to use brackets when doing so to avoid confusion.
Reply 2
Original post by ghost88
Solve the equation. 25^x = 5^4x+1

Can someone please help me and explain how to get to the answer? Thanks.


Since 25=5225 = 5^2 then 25x=(52)x=52x25^x = \left(5^2\right)^x = 5^{2x}

So your equation reduces to

54x−52x+1=0\displaystyle 5^{4x} - 5^{2x} + 1 = 0

A simple substitution of a=52xa = 5^{2x} yields a2−a+1=0a^2 - a + 1 =0

Which is a simple quadratic, solve and then back-substiute.
Original post by Zacken
Since 25=5225 = 5^2 then 25x=(52)x=52x25^x = \left(5^2\right)^x = 5^{2x}
So your equation reduces to
54x−52x+1=0\displaystyle 5^{4x} - 5^{2x} + 1 = 0
A simple substitution of a=52xa = 5^{2x} yields a2−a+1=0a^2 - a + 1 =0
Which is a simple quadratic, solve and then back-substiute.
It's even simpler than that:
25^x = 5^4x+1
if 25^x=5^2x
then 2x=4x+1
therefore you can -2x and -1 hence, 2x=-1
then /2 giving x=-1/2
Reply 4
Original post by 04MR17
It's even simpler than that:
25^x = 5^4x+1
if 25^x=5^2x
then 2x=4x+1
therefore you can -2x and -1 hence, 2x=-1
then /2 giving x=-1/2


Ah, I think we might be at a cross-roads here. I'm reading the equation as 25x=54x+1\displaystyle 25^{x} = 5^{4x} + 1, you're reading it as 25x=54x+1\displaystyle 25^x = 5^{4x+1} - it's up to the OP to clarify here.
Original post by Zacken
Ah, I think we might be at a cross-roads here. I'm reading the equation as 25x=54x+1\displaystyle 25^{x} = 5^{4x} + 1, you're reading it as 25x=54x+1\displaystyle 25^x = 5^{4x+1} - it's up to the OP to clarify here.
I've been doing these last week, if it's C1 AS it'll probably be my way. If it's anything above you'll be right I Reckon Zacken.
Reply 6
Original post by 04MR17
I've been doing these last week, if it's C1 AS it'll probably be my way. If it's anything above you'll be right I Reckon Zacken.


In either case, I'll be annoyed at the OP for his ambiguity. :tongue:
Original post by Zacken
In either case, I'll be annoyed at the OP for his ambiguity. :tongue:
Even so, the winner gets a rep.
Reply 8
Original post by 04MR17
Even so, the winner gets a rep.


May the best guesser win. :laugh:
I don't mind if you get the rep. :smile:
Original post by ghost88
Solve the equation. 25^x = 5^4x+1

Can someone please help me and explain how to get to the answer? Thanks.


Use logs , or rules of indicies
25^x is the same as 5^2
So x^2 = 4x +1
Then reaarange for quadratic and solve
Make both powers in base 5 and put the powers equal then solve
Reply 11
The ghost88 has become a ghost ...
Reply 12
Sorry guys, I moved on to Economics and forgot to check :biggrin:. And Yeah its C1.

Thanks to all for replying

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