If 2^(x+y)= 64 and 128^(x-y) = 2 , then what is the value of x ?

The correct answer is Option (2) → 43/14

Write every number as a power of 2; two equal powers of the same base have equal exponents.

The two equations (64 = 2⁶, 128 = 2⁷):

• \(2^{x+y}=2^{6}\), so \(x+y=6\)        (1)

• \(2^{7(x-y)}=2^{1}\), so \(\displaystyle x-y=\frac{1}{7}\)        (2)

Finding \(x\) (adding (1) and (2), the \(y\) terms cancel):

• \(\displaystyle 2x=6+\frac{1}{7}=\frac{43}{7}\)

• \(\displaystyle x=\frac{43}{14}\)