Question

(2x+1)+ 3 (2x+1)4, x+-1_2
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Answer 1

4^x -3^(x-1/2) =3^(x+1/2) -2^(2x-1)

=> 4^x +2^(2x-1) = 3^(x-1/2) +3^(x+1/2)

2^2x +2^2x * 2^-1 = (3^x-1/2 )* 3^x + 3^(1/2)* 3^x

=> 2^2x (1+1/2) = 3^x ( 3^(-1/2) + 3^(1/2))

=> 4^x * (3/2)= 3^ x * ( 4 / sqrt(3))

=> 4^x / 3^x = 8/ (3 sqrt(3)) = 8 sqrt(3) / 9

=> (4/3)^x = 8 sqrt(3) /9

x Log (4/3) = Log 8 + Log sqrt(3) - Log 9

=> x = (3 Log 2 +(1/2) Log 3 - 2 Log 3)/ ( 2 Log2 - Log 3)

=> x= (3 Log2 -3/2 Log 3) / ( 2Log 2 -Log 3)

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Answer 2

Answer:

(3x)+3( 3x ) 4x1/2

(6x) (3x) 4x1/2

(18x) 4x1/2

(18x) 4/2

4x9

= 36x ans.

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