Short answer x = 11/3 Step One Change 64 to a power of 4 [tex] \text{64 = 4}^{4} [/tex]
Step Two Include 2x - 4 as part of your power. So far you are only working on the right side of the problem.
[tex] (x^{4*(2x - 4)} [/tex]
Step Three The bases are the same so you can equate the powers. 2x + 6 = 4(2x - 4)
Step Four Remove the brackets on the right. 2x + 6 = 8x - 16
Step five Collect like terms. Begin by adding 14 to both sides. 2x + 6 + 16 = 8x Subtract 2x from both sides. 22 = 8x - 2x 22 = 6x Divide by 6 22/6 = x x = 3.666333 or 3 2/3 or 11/3
Check Left hand side 4^(2*11/3 + 6) 4^(22/3 + 6) 4^(22/3 + 18/3) 4^(40/3)
Right Side 64^(2*11/3 - 4) 64^(22/3 - 4) 64^(22/3 - 12/3) 64^(10/3) There is something we can do without figuring out what this is. 64 = 4^4 4^(4*10/3) 4^(40/3) which is the same as the left side