Question

Please solve i got 3 but i’m not sure

Answer 1

Short answer x = 11/3
Step One
Change 64 to a power of 4

`\text{64 = 4}^(4)`

Step Two
Include 2x - 4 as part of your power. So far you are only working on the right side of the problem.


`(x^(4*(2x - 4))`

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

Answer x = 11/3 <<<<<