Answer:
0.8
Step-by-step explanation:
You are given the equation
[tex]\left(\dfrac{1}{64}\right)^{0.5x-3}=8^{9x-2}[/tex]
First note that
[tex]\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}[/tex]
Now
[tex]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[/tex]
