Solve an equation

Question

http://prntscr.com/fnyt67

Answer 1

The equation is equivalent to:  [2^x{4^x (2^-3)^1/x}^1/3]^1/2 = 4(2)^1/3

 

        [2^x{2^2x2^-3/x}^1/3]^1/2 = 2²2^1/3

 

        [2^x{2^2x-3/x}^1/3]^1/2 = 2^7/3

 

        [2^x{2^2x/3-1/x}]^1/2 = 2^7/3

 

        [2^{5x/3 - 1/x}]^1/2 = 2^7/3

 

         2^{5x/6 - 1/(2x)} = 2^7/3

 

5x/6 - 1/(2x) = 7/3

 

Multiply by the LCD, 6x, to get 5x² - 3 = 14x

 

5x² - 14x - 3 = 0

 

(5x+1)(x-3) = 0

 

x = -1/5 or 3

 

Answer 2

√(2^x 3√(4^x (0.125)^1/x)) = 4 ³√2

2^x 3√4^x (0.125)^1/x) = 16 ³√4

2^3x (4^x (0.125)^1/x) = 4096 · 4

2^3x (4^x (0.125)^1/x) = 16384

2^3x 2^2x 0.125^1/x = 16384

2^5x 0.125^1/x = 16384

0.125^1/x = 16384 / 2^5x

ln 0.125^1/x = ln 16384 - ln 2^5x

 

Can you finish?