Find x, if 8x–2 x \(\big(\frac12\big)^{4-3x}\) = (0.0625)x(a) 0

1.	Find x, if 8x–2 x \(\big(\frac12\big)^{4-3x}\) = (0.0625)x(a) 0 (b) 4 (c) 2 (d) 1
Answer» (d) 1 8^x–2x \(\big(\frac12\big)^{4-3x}\) = (0.0625)^x (2³)^{x – 2} x (2^–1)^4–3x = \(\big(\frac{625}{10000}\big)^x\) ⇒ 2^3x-6 x 2^-4+3x = \(\big(\frac{1}{16}\big)^x\) = (2^-4)^x = 2^-4x ⇒ 2^3x-6-4+3x = 2^-4x ⇒ 2^{6x – 10} = 2^{– 4x} ⇒ 6x – 10 = – 4x ⇒ 10x = 10 ⇒ x = 1.

Find x, if 8x–2 x \(\big(\frac12\big)^{4-3x}\) = (0.0625)x(a) 0 (b) 4 (c) 2 (d) 1

Answer»

(d) 1

8^x–2x \(\big(\frac12\big)^{4-3x}\) = (0.0625)^x

(2³)^{x – 2} x (2^–1)^4–3x = \(\big(\frac{625}{10000}\big)^x\)

⇒ 2^3x-6 x 2^-4+3x = \(\big(\frac{1}{16}\big)^x\) = (2^-4)^x = 2^-4x

⇒ 2^3x-6-4+3x = 2^-4x

⇒ 2^{6x – 10} = 2^{– 4x}

⇒ 6x – 10 = – 4x

⇒ 10x = 10 ⇒ x = 1.