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

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Answer 1 · 2018-03-04T16:30:26

$x=1/6$

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:

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

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