Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    8
    ReputationRep:
    Two graphs y= (1/3)^x and y= 2(3)^x intersect at a point. Find the coordinates. PLS explain this at every step since the mark sheme i looked at made no sense whatsoever.


    Thanks
    Offline

    2
    ReputationRep:
    Take logs of both sides and equate:

    log[(1/3)^x] = log[2(3)^x]
    log[(1/3)^x] = log2 + log[(3)^x] , using the addition of logs law
    xlog(1/3) = log2 + xlog3 , using another one of the log laws
    xlog1 - xlog3 = log2 + xlog3

    log1 = 0

    => 2xlog3 = -log2
    x = - log2 / 2log3
    Offline

    15
    ReputationRep:
    (Original post by mockelinho)
    Take logs of both sides and equate:

    log[(1/3)^x] = log[2(3)^x]
    log[(1/3)^x] = log2 + log[(3)^x] , using the addition of logs law
    xlog(1/3) = log2 + xlog3 , using another one of the log laws
    xlog1 - xlog3 = log2 + xlog3

    log1 = 0

    => 2xlog3 = -log2
    x = - log2 / 2log3
    good edit. I was just about to point the - out.
    • Thread Starter
    Offline

    8
    ReputationRep:
    Thanks a lot!! I was trying that out whilst practicing but kept getting it wrong. Got it now. Now in the question it says that show that the y coordinate is [square root]2

    how do they get tht?
    Offline

    15
    ReputationRep:
    (Original post by Mohit_C)
    Thanks a lot!! I was trying that out whilst practicing but kept getting it wrong. Got it now. Now in the question it says that show that the y coordinate is [square root]2

    how do they get tht?
    Having had a look it would be easiest to do it in this way:
    logy = -x log3
    log y = (-log2/2log3) (-log3)
    log y = 1/2 log 2
    log y = log21/2
    y = rt2
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: April 10, 2006
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
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.