Turn on thread page Beta
    • Thread Starter
    Offline

    8
    ReputationRep:
    Solve the equation. 25^x = 5^4x+1

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

    7
    ReputationRep:
    25 can be simplified into a power of 5. Make sure to use brackets when doing so to avoid confusion.
    Offline

    22
    ReputationRep:
    (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 = 5^2 then 25^x = \left(5^2\right)^x = 5^{2x}

    So your equation reduces to

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

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

    Which is a simple quadratic, solve and then back-substiute.
    • Community Assistant
    Offline

    22
    ReputationRep:
    Community Assistant
    (Original post by Zacken)
    Since 25 = 5^2 then 25^x = \left(5^2\right)^x = 5^{2x}
    So your equation reduces to
    \displaystyle 5^{4x} - 5^{2x} + 1 = 0
    A simple substitution of a = 5^{2x} yields a^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
    Offline

    22
    ReputationRep:
    (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 \displaystyle 25^{x} = 5^{4x} + 1, you're reading it as \displaystyle 25^x = 5^{4x+1} - it's up to the OP to clarify here.
    • Community Assistant
    Offline

    22
    ReputationRep:
    Community Assistant
    (Original post by Zacken)
    Ah, I think we might be at a cross-roads here. I'm reading the equation as \displaystyle 25^{x} = 5^{4x} + 1, you're reading it as \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.
    Offline

    22
    ReputationRep:
    (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.
    • Community Assistant
    Offline

    22
    ReputationRep:
    Community Assistant
    (Original post by Zacken)
    In either case, I'll be annoyed at the OP for his ambiguity.
    Even so, the winner gets a rep.
    Offline

    22
    ReputationRep:
    (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.
    Offline

    2
    ReputationRep:
    (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
    Offline

    2
    ReputationRep:
    Make both powers in base 5 and put the powers equal then solve
    Offline

    19
    ReputationRep:
    The ghost88 has become a ghost ...
    • Thread Starter
    Offline

    8
    ReputationRep:
    Sorry guys, I moved on to Economics and forgot to check . And Yeah its C1.

    Thanks to all for replying
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: September 16, 2015

University open days

  • University of Bradford
    All faculties Undergraduate
    Wed, 21 Nov '18
  • Buckinghamshire New University
    All Faculties Postgraduate
    Wed, 21 Nov '18
  • Heriot-Watt University
    All Schools Postgraduate
    Wed, 21 Nov '18
Poll
Black Friday: Yay or Nay?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.