What is log_{3}((100)/(27x)) ?

The solution to log_{3}((100)/(27x)) is 2log_{3}(10)-3-log_{3}(x)

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simplify log_{3}((100)/(27x))

simplify

lo g_{3} (\frac{100}{27 x})

2 lo g_{3} (10) - 3 - lo g_{3} (x)

Solution steps

lo g_{3} (\frac{100}{27 x})

Apply log rule:

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

lo g_{3} (\frac{100}{27 x}) = lo g_{3} (100) - lo g_{3} (27 x)

= lo g_{3} (100) - lo g_{3} (27 x)

lo g_{3} (100) = 2 lo g_{3} (10)

lo g_{3} (27 x) = 3 + lo g_{3} (x)

= 2 lo g_{3} (10) - (3 + lo g_{3} (x))

Apply the distributive law:

- (a + b) = - a - b

- (3 + lo g_{3} (x)) = - 3 - lo g_{3} (x)

= 2 lo g_{3} (10) - 3 - lo g_{3} (x)

lo g_{5} (\frac{x}{125})

lo g_{10} (2 x + 1) - lo g_{10} (x)

- lo g_{10} (1.8 \cdot 1 0^{- 4})

\frac{5}{2} ln (\frac{15}{4})

What is log_{3}((100)/(27x)) ?
The solution to log_{3}((100)/(27x)) is 2log_{3}(10)-3-log_{3}(x)