Question

How do you solve `x= \log _ { 10} \root(6) { 10}`?

Answer 1

`x=1/6`

Explanation:

We know that

`log_(10)(10^a) = a`

So it would be nice to get our equation in a form like that. We need to recall that a root is the same as the reciprocal of the power, i.e.:

`\root(b)(y) = y^(1/b)`

Therefore:

`x = log_(10)(\root(6)(10))=log_10(10^(1/6)) = 1/6`