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1. 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
2. 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
3. (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.
4. 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?
5. (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

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