1) 2^4x-14=1/642^4x = 1/64 + 142^4x = 1/64 + 896/642^4x = 897/642^4x = 14.015625
Taking the logarithm of both sides with base 2:4x = log2(14.015625)4x = 3.81086x = 0.952715
2) (1/2)^4x-14=1/64(1/2)^(4x-14)=1/64(1/2)^(4x-14)=2^-6
Since the bases are the same, we can equate the exponents:4x-14 = -64x = -6 + 144x = 8x = 2
1) 2^4x-14=1/64
2^4x = 1/64 + 14
2^4x = 1/64 + 896/64
2^4x = 897/64
2^4x = 14.015625
Taking the logarithm of both sides with base 2:
4x = log2(14.015625)
4x = 3.81086
x = 0.952715
2) (1/2)^4x-14=1/64
(1/2)^(4x-14)=1/64
(1/2)^(4x-14)=2^-6
Since the bases are the same, we can equate the exponents:
4x-14 = -6
4x = -6 + 14
4x = 8
x = 2