If 343 to the x th power is equal to 49 raised to the 4 minus x power , what is the value of x ?

Rewrite both numbers as powers of 7: 343 = 7³ and 49 = 7². Then 343ˣ = 49⁽⁴⁻ˣ⁾ becomes 7³ˣ = 7⁽⁸⁻²ˣ⁾, so the exponents must be equal: 3x = 8 − 2x. Solving gives 5x = 8, or x = 8/5, which is choice D.

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