Find the value of x, if 2^1+x-2^1-x=3
Answers
Answer:
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Step-by-step explanation:
If 2^(x+1) = 3^(1-x) Then find the value of 'x'?
If 2^(x+1) = 3^(1-x) Then find the value of 'x'?
Let 2^( x + 1 ) - 3^( 1 - x ) = 0 be Equation(1).
Take Logs of both sides of Equation(1).
Log[ 2^( x + 1 ) ] - Log[ 3^( 1- x ) ] = 0 Equation(2).
Rearranging Equation(2).
( x + 1 )Log( 2 ) - ( 1 - x )Log( 3 ) = 0 or
( x + 1 )Log( 2 ) = ( 1 - x )Log( 3 ) or
( x + 1 )/( 1 - x ) = Log( 3 )/Log ( 2 ) or
( x + 1 )/( 1 - x ) = 1.584962501 Equation(3).
Therefore
( x + 1 ) = ( 1.584962501 )•( 1 - x ) or
x + ( 1.584962501x ) = ( 1.584962501 - 1 ) or
( 2.584962501 )x = ( 0.584962501 ) or
x = ( 0.584962501 )/( 2.584962501 ) or
x = 0.2262943856
Check
2^( x+1 ) = 3^( 1-x )
2^( 1.2262943856 ) = 3^( 1 - 0.2262943856 )
2^( 1,2262943856 ) = 3^( 0.7737056 )
2.33965269 = 2.33965268
Therefore x as calculated is correct.