What is log_{3}(x)-8log_{3}(x+8) ?

The solution to log_{3}(x)-8log_{3}(x+8) is log_{3}(x/((x+8)^8))

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simplify log_{3}(x)-8log_{3}(x+8)

simplify

lo g_{3} (x) - 8 lo g_{3} (x + 8)

lo g_{3} (\frac{x}{( x + 8 ) ^{8}})

Solution steps

lo g_{3} (x) - 8 lo g_{3} (x + 8)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 lo g_{3} (x + 8) = lo g_{3} ((x + 8)^{8})

= lo g_{3} (x) - lo g_{3} ((x + 8)^{8})

Apply log rule:

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

lo g_{3} (x) - lo g_{3} ((x + 8)^{8}) = lo g_{3} (\frac{x}{( x + 8 ) ^{8}})

= lo g_{3} (\frac{x}{( x + 8 ) ^{8}})

ln (2120) - ln (2120 - 10000) - ln (- \frac{1}{249})

lo g_{10} (x) + \frac{1}{7} lo g_{10} (y)

(1 - (2 \cdot 0.93)) \cdot ln (\frac{1 - 0.93}{0.93})

lo g_{e} (\frac{e ^{a + b \cdot x} - f ( x )}{f ( x )})

ln (\frac{y}{x ^{2 n}} \cdot e^{\frac{- m}{x}})

What is log_{3}(x)-8log_{3}(x+8) ?
The solution to log_{3}(x)-8log_{3}(x+8) is log_{3}(x/((x+8)^8))