What is log_{3}((81)/(x^2+5)) ?

The solution to log_{3}((81)/(x^2+5)) is 4-log_{3}(x^2+5)

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simplify log_{3}((81)/(x^2+5))

simplify

lo g_{3} (\frac{81}{x ^{2} + 5})

4 - lo g_{3} (x^{2} + 5)

Solution steps

lo g_{3} (\frac{81}{x ^{2} + 5})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{81}{x ^{2} + 5}) = lo g_{3} (81) - lo g_{3} (x^{2} + 5)

= lo g_{3} (81) - lo g_{3} (x^{2} + 5)

lo g_{3} (81) = 4

= 4 - lo g_{3} (x^{2} + 5)

- lo g_{10} (\frac{1}{x})

lo g_{5} (125 x)

lo g_{3} (x^{2} - 4) - lo g_{3} (x + 2)

lo g_{10} (\frac{a ^{2}}{b ^{4} c})

lo g_{3} (5) + 5 lo g_{3} (2)

What is log_{3}((81)/(x^2+5)) ?
The solution to log_{3}((81)/(x^2+5)) is 4-log_{3}(x^2+5)