Problem: The real value of xxx such that 64x−164^{x-1}64x−1 divided by 4x−14^{x-1}4x−1 equals 2562x256^{2 x}2562x is:
Answer Choices:
A. −23-\dfrac{2}{3}−32
B. −13-\dfrac{1}{3}−31
C. 000
D. 14\dfrac{1}{4}41
E. 38\dfrac{3}{8}83 Solution:
64x−1÷4x−1=43x−3÷4x−1=42x−264^{x-1} \div 4^{x-1}=4^{3 x-3} \div 4^{x-1}=4^{2 x-2}64x−1÷4x−1=43x−3÷4x−1=42x−2. Since 2562x=48x,42x−2=48x∴2x−2=8x,x=−13256^{2 x}=4^{8 x}, 4^{2 x-2}=4^{8 x} \quad \therefore 2 x-2=8 x, x=-\dfrac{1}{3}2562x=48x,42x−2=48x∴2x−2=8x,x=−31.