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

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Answer 1 · 2018-03-04T16:30:26

$x = \frac{1}{6}$ $x=1/6$

We know that

${log}_{10} (10^{a}) = a$ $log_(10)(10^a) = a$

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.:

$\sqrt[b]{y} = y^{\frac{1}{b}}$ $\root(b)(y) = y^(1/b)$

Therefore:

$x = {log}_{10} (\sqrt[6]{10}) = {log}_{10} (10^{\frac{1}{6}}) = \frac{1}{6}$ $x = log_(10)(\root(6)(10))=log_10(10^(1/6)) = 1/6$

How do you solve x= \log _ { 10} \root(6) { 10}x=log106√10x= \log _ { 10} \root(6) { 10}?