What is log_{3}((81)/(sqrt(x-1))) ?

The solution to log_{3}((81)/(sqrt(x-1))) is 4-log_{3}(sqrt(x-1))

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simplify log_{3}((81)/(sqrt(x-1)))

simplify

lo g_{3} (\frac{81}{x - 1})

4 - lo g_{3} (x - 1)

Solution steps

lo g_{3} (\frac{81}{x - 1})

Apply log rule:

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

lo g_{3} (\frac{81}{x - 1}) = lo g_{3} (81) - lo g_{3} (x - 1)

= lo g_{3} (81) - lo g_{3} (x - 1)

lo g_{3} (81) = 4

= 4 - lo g_{3} (x - 1)

lo g_{4} (\frac{a ( x + 3 ) ^{3}}{a - b ^{3}})

ln (x) + \frac{4}{3} ln (y) - \frac{5}{3} ln (z) - \frac{1}{3} ln (x)

ln (\frac{6 x}{x ^{2} - 9})

lo g_{4} (19 b^{6} c)

ln (\frac{e ^{7}}{15})

What is log_{3}((81)/(sqrt(x-1))) ?
The solution to log_{3}((81)/(sqrt(x-1))) is 4-log_{3}(sqrt(x-1))