Question

2^x+1=3^1-x and find the x value​

Answer 1

Answer:

x = 0.2262943856

Step-by-step explanation:

Solution,

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

( x + 1 )Log( 2 ) = ( 1 - x )Log( 3 )

( x + 1 )/( 1 - x ) = Log( 3 )/Log ( 2 )

( x + 1 )/( 1 - x ) = 1.584962501 Equation(3).

Therefore

( x + 1 ) = ( 1.584962501 )•( 1 - x )

x + ( 1.584962501x ) = ( 1.584962501 - 1 )

( 2.584962501 )x = ( 0.584962501 )

x = ( 0.584962501 )/( 2.584962501 )

x = 0.2262943856