Question

$slove \: {2}^{x + 1} = {3}^{1 - x}$
​

Answer 1

Answer:

2.33965268

Step-by-step explanation:

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.