Question

How do you solve `log_8 5 -log_8(x-6)=1`?

Answer 1

`x=53/8 or 6 5/8`

Explanation:

Remembering that
`color(white)("XXX")color(blue)(log_b(p) - log_b(q)=log_b (p/q))`
and that
`color(white)("XXX"color(magenta)(log_b(b) = 1)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)(log_8 5 - log_8 (x-6))=color(magenta)(1)`

can be rewritten as
`color(white)("XXX")color(blue)(log_8(5/(x-6))) =color(magenta)( log_8 8)`

which implies
`color(white)("XXX")5/(x-6)=8`

`color(white)("XXX")rarr5=8x-48`

`color(white)("XXX")rarr 8x=53`

`color(white)("XXX")rarr x=53/8`