Question

If 343* = 494-x, what is the value of x? 5/8 8/5 2 8

Answer 1

Answer: $\frac{8}{5}$

Step-by-step explanation:

343 is equal to 7 to the power of 3.

49 is equal to 7 to the power of 2.

You can then make the equation:

$(7^{3})^x = (7^2)^{4-x}$

The powers law means if something is to the power of something, it is multiplied.

So, we can remove the 7 and make the equation:

3x = 2(4-x)

3x = 8 - 2x

5x = 8

x = $\frac{8}{5}$

You can verify this by plugging it in,

$343^{8/5} = 11388.6066$

$49^{4-(8/5)} = 11388.6066$