Question

How do you solve `log_7 x - log_7(x-2) = log_7 11`?

Answer 1

`x = 11/5`

Explanation:

using the 'law of logs': `log x - log y = log(x/y)`

then `log_7 x - log_7 (x - 2 ) = log_7(x/(x-2))`

and so `log_7(x/(x-2)) = log_7 11`

now if `log_b a = log_b c color(black)(" then a = c ")`

hence `x/(x-2) = 11`

so 11(x-2) = x → 11x - 22 = x → 10x =22 → `x = 11/5`