if (2/9)power x-1=(9/2)power x-5 find the value of x
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Solution:
*********************************
We know the Exponential laws :
i ) ( a/b )ⁿ = ( b/a )^-1
ii ) If a^m = a^n then m = n
**********************************
Now ,
( 2/9 )^(x-1) = ( 9/2 )^(x-5)
=> ( 9/2 )^-(x-1) = ( 9/2 )^x-5
=> - ( x - 1 ) = x - 5
=> 0 = x - 5 + x - 1
=> 0 = 2x - 6
=> 2x - 6 = 0
=> 2x = 6
=> x = 6/2
x = 3
Therefore ,
x = 3
••••
*********************************
We know the Exponential laws :
i ) ( a/b )ⁿ = ( b/a )^-1
ii ) If a^m = a^n then m = n
**********************************
Now ,
( 2/9 )^(x-1) = ( 9/2 )^(x-5)
=> ( 9/2 )^-(x-1) = ( 9/2 )^x-5
=> - ( x - 1 ) = x - 5
=> 0 = x - 5 + x - 1
=> 0 = 2x - 6
=> 2x - 6 = 0
=> 2x = 6
=> x = 6/2
x = 3
Therefore ,
x = 3
••••
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