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

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

4^x  - 3^x * 3^-1/2 = 3^x * 3^1/2 - 2^2x * 2^-1

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

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

3/2 * 2^2x =  2.3094 * 3^x

ln 1.5 + 2x ln 2 = ln 2.3094 + x ln 3

2x ln 2 - x ln3 = ln 2,3094 - ln 1.5

1.3863 x - 1.0986 x =  0.4315

0.2877x = 0.4315

x =  1.5   Answer

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right

1. minimum

2. 6400

3. eight

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