What is 1/2 log_{3}(x)-2log_{3}(y+8) ?

The solution to 1/2 log_{3}(x)-2log_{3}(y+8) is log_{3}((x^{1/2})/((y+8)^2))

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simplify 1/2 log_{3}(x)-2log_{3}(y+8)

simplify

\frac{1}{2} lo g_{3} (x) - 2 lo g_{3} (y + 8)

lo g_{3} (\frac{x ^{\frac{1}{2}}}{( y + 8 ) ^{2}})

Solution steps

\frac{1}{2} lo g_{3} (x) - 2 lo g_{3} (y + 8)

Apply log rule:

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

\frac{1}{2} lo g_{3} (x) = lo g_{3} (x^{\frac{1}{2}})

= lo g_{3} (x^{\frac{1}{2}}) - 2 lo g_{3} (y + 8)

Apply log rule:

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

2 lo g_{3} (y + 8) = lo g_{3} ((y + 8)^{2})

= lo g_{3} (x^{\frac{1}{2}}) - lo g_{3} ((y + 8)^{2})

Apply log rule:

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

lo g_{3} (x^{\frac{1}{2}}) - lo g_{3} ((y + 8)^{2}) = lo g_{3} (\frac{x ^{\frac{1}{2}}}{( y + 8 ) ^{2}})

= lo g_{3} (\frac{x ^{\frac{1}{2}}}{( y + 8 ) ^{2}})

- lo g_{10} (2.4 \cdot 1 0^{- 7})

ln (\frac{3.7}{1.2})

x - ln (3 x)

\frac{9}{14} lo g_{2} (\frac{9}{14}) + \frac{5}{14} lo g_{2} (\frac{5}{14})

- lo g_{10} (2.5 \cdot 1 0^{- 6})

What is 1/2 log_{3}(x)-2log_{3}(y+8) ?
The solution to 1/2 log_{3}(x)-2log_{3}(y+8) is log_{3}((x^{1/2})/((y+8)^2))