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

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

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

expand

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_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

lo g_{3} (27) = 3

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

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

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

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

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

ln (\frac{4 e ^{6}}{7 y})

lo g_{7} (x) - lo g_{7} (x^{2})

ln (\frac{x}{b})

\frac{1}{2} lo g_{10} (3) - \frac{1}{2} lo g_{10} (12)

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