MATH SOLVE

4 months ago

Q:
# please solve i got 3 but i’m not sure

Accepted Solution

A:

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

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

Answer x = 11/3 <<<<<