Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    So the question is 2^(2x) + 2^x - 6 = 0. Can someone explain why I can't put logs in the equation? like e.g make it (2x)log2 + xlog2 - log6 = 0. Int he answers what theyve done is theyve factorised it as if it was a quadratic. :s
    Offline

    16
    ReputationRep:
    (Original post by tetra-s)
    So the question is 2^(2x) + 2^x - 6 = 0. Can someone explain why I can't put logs in the equation? like e.g make it (2x)log2 + xlog2 - log6 = 0.
    If you have

    a+b=c

    You cannot do

    log(a) + log(b) = log(c)

    Any more than you can apply any other function

    Eg

    You cannot do

    a^2 + b^2 = c^2
    Offline

    16
    ReputationRep:
    (Original post by tetra-s)
    In the answers what theyve done is theyve factorised it as if it was a quadratic. :s
    It is a quadratic

    2^{2x} + 2^x - 6 = 0

    2^{2x} = (2^x)^2

    So you have

    (2^x)^2 + 2^x - 6 = 0

    Which is the equivalent of

    y^2 + y - 6 = 0
    • Political Ambassador
    Offline

    3
    ReputationRep:
    Political Ambassador
    ^More specifically,

    \ln(a) + \ln(b) = \ln(ab) \neq \ln(a+b).
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ah I see, makes sense now! thanks everyone
    Offline

    16
    ReputationRep:
    (Original post by nm786)
    yeah with these kind of questions, always make sure you end up with a quadratic so that you can factorise and then easily solve for x.
    But with this one either complete the square or use the quadratic formula because b^2-4ac \neq n^2.
    Actually it does factorise
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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

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.