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How many number of solutions of log[5](x-1)=log[2](x-3)?(jee)
there are various methods by which you can solve this problem,
i''ll be following the objective approach as you are mainly concerned for jee,
the fastest method for solving this problem is to consider the graph of logarithmic function!!
yes you got it a DECREASING curve streching from - infinity to +infinity
now for log5 (x-1) at x=2 we get the curve crossing the X axis
similary for x=4 we get the other curve crossing the X axis
now if you consider the poitn x=6
log5 (x-1) = 1
and log2 (x-1) = log2 5 which is definitly greater than 1
if you move forward log2x > log5x
so the curve will never intersect again
CLEARLY THEIR EXIST ONLY ONE SOLUTION!! that is between 2 and 6
ALTHOUGH THIS APPROACH MAY SEEM TO YOU RATHER ILLOGICAL
BUT BEILIVE ITS THE FASTEST!!!
Plot individual graphs of RHS and LHS, number of point of intersection represent the number of solution of the equation,
Best of luck!
May god bless you!
1
x=11 only satisfies the condition.hence only one value is possible
log[5](x-1)=log[2](x-3)
taking anti log,
5x-5=2x-6
3x=-1
x=-1/3
this value of x does not satisfy the domain of lag so this equation has no solution.
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