Question

Solve (1/64)^0.5x-3 =8^9x-2​

Answer 1

0.8

Explanation:

You are given the equation

`\left((1)/(64)\right)^(0.5x-3)=8^(9x-2)`

First note that

`(1)/(64)=(1)/(2^6)=2^(-6)\\ \\\left((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=(24)/(30)=(8)/(10)=0.8`