Logarithmic Domains

Algebra Level 4

$\large f(x)=\sqrt {\log_{0.3} (\log_{2} x})$ Find the domain of the function above.

(2, \infty )

[2, \infty )

\mathbb R

(1,2 ]

[1,2 ]

(0, \infty )

1 solution

Aquilino Madeira
Jul 23, 2015

$\begin{array}{l} {D_f} = \left\{ {x \in \Re :{{\log }_{0,3}}\left( {{{\log }_2}x} \right) \ge 0\; \wedge \;x > 0\; \wedge \;{{\log }_2}x > 0} \right\}\\ {D_f} = \left\{ {x \in \Re :{{\log }_2}x \le {{(0,3)}^0}\; \wedge \;x > 0\; \wedge \;x > {2^0}} \right\}\\ {D_f} = \left\{ {x \in \Re :x \le 2\; \wedge \;x > 0\; \wedge \;x > 1} \right\}\\ {D_f} = \left] {1,2} \right] \end{array}$

I don't understand why the square root has to be >= 0. There is something implicit disallowing complex numbers, I guess. Is this standard in finding the domain?

I would have thought the correct range is (1, inf) since the square root can handle any domain (assuming imaginary numbers are allowed).

Mike Williamson - 3 years, 7 months ago

Logarithmic Domains

1 solution

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