Question

Solve (1/64)^0.5x-3 =8^9x-2​

Answer 1

Answer:

0.8

Step-by-step explanation:

You are given the equation

$\left(\dfrac{1}{64}\right)^{0.5x-3}=8^{9x-2}$

First note that

$\dfrac{1}{64}=\dfrac{1}{2^6}=2^{-6}\\ \\\left(\dfrac{1}{64}\right)^{0.5x-3}=(2^{-6})^{0.5x-3}=2^{-6\cdot (0.5x-3)}=2^{-3x+18}\\ \\8=2^3\\ \\8^{9x-2}=(2^3)^{9x-2}=2^{3\cdot (9x-2)}=2^{27x-6}$

Now

$2^{-3x+18}=2^{27x-6}\\ \\-3x+18=27x-6\\ \\-3x-27x=-6-18\\ \\-30x=-24\\ \\x=\dfrac{24}{30}=\dfrac{8}{10}=0.8$