What is 1/(log_{2)(6)}+1/(log_{108)(6)} ?

The solution to 1/(log_{2)(6)}+1/(log_{108)(6)} is 1/(1+log_{2)(3)}+1/(log_{108)(6)}

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simplify 1/(log_{2)(6)}+1/(log_{108)(6)}

simplify

\frac{1}{lo g _{2} ( 6 )} + \frac{1}{lo g _{108} ( 6 )}

\frac{1}{1 + lo g _{2} ( 3 )} + \frac{1}{lo g _{108} ( 6 )}

Solution steps

\frac{1}{lo g _{2} ( 6 )} + \frac{1}{lo g _{108} ( 6 )}

Factor the number:

6 = 2 \cdot 3

= \frac{1}{lo g _{2} ( 2 \cdot 3 )} + \frac{1}{lo g _{108} ( 6 )}

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (2 \cdot 3) = lo g_{2} (2) + lo g_{2} (3)

= \frac{1}{lo g _{2} ( 2 ) + lo g _{2} ( 3 )} + \frac{1}{lo g _{108} ( 6 )}

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= \frac{1}{1 + lo g _{2} ( 3 )} + \frac{1}{lo g _{108} ( 6 )}

\frac{3}{x + 1} + \frac{4}{x}

\frac{sec ( x )}{cos ( x )} - \frac{tan ( x )}{cot ( x )}

\frac{- 7 + 19 i}{4 - 5 i}

46 \cdot 6

- (x - 1)

What is 1/(log_{2)(6)}+1/(log_{108)(6)} ?
The solution to 1/(log_{2)(6)}+1/(log_{108)(6)} is 1/(1+log_{2)(3)}+1/(log_{108)(6)}