Question

Solve 3 log6 2 + 2 log6 3 − log6 x = 2.

Answer 1

x = 2

Explanation:

I just took the test.

Answer 2

`D:x \ \textgreater \ 0\\\\3\log_62+2\log_63-\log_6x=2\\-----------------------\\Use:\\\log_ab=c\iff a^c=b\\\log_ab+\log_ac=\log_a(bc)\\\log_ab-\log_ac=\log_a((b)/(c))\\\log_ab^c=c\log_ab\\-----------------------\\\log_62^3+\log_63^2-\log_6x=2\\\\\log_68+\log_69-\log_6x=\log_66^2\\\\\log_6(8\cdot9)-\log_6x=\log_636\\\\\log_672-\log_6x=\log_636\\\\\log_6(72)/(x)=\log_636\iff(72)/(x)=36\\\\(x)/(72)=(1)/(36)\ \ \ \ \ |multiply\ both\ sides\ by\ 72\\\\x=(72)/(36)\\\\\boxed{x=2}\in D`