What is expand log_{10}((sqrt(x))/(10000y^9)) ?

The solution to expand log_{10}((sqrt(x))/(10000y^9)) is log_{10}(sqrt(x))-4-9log_{10}(y)

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expand log_{10}((sqrt(x))/(10000y^9))

expand

lo g_{10} (\frac{x}{10000 y ^{9}})

lo g_{10} (x) - 4 - 9 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{10000 y ^{9}})

Apply log rule:

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

lo g_{10} (\frac{x}{10000 y ^{9}}) = lo g_{10} (x) - lo g_{10} (10000 y^{9})

= lo g_{10} (x) - lo g_{10} (10000 y^{9})

Apply log rule:

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

lo g_{10} (10000 y^{9}) = lo g_{10} (10000) + lo g_{10} (y^{9})

= lo g_{10} (x) - (lo g_{10} (y^{9}) + lo g_{10} (10000))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (y^{9}) = 9 lo g_{10} (y)

= lo g_{10} (x) - (lo g_{10} (10000) + 9 lo g_{10} (y))

lo g_{10} (10000) = 4

= lo g_{10} (x) - (9 lo g_{10} (y) + 4)

- (4 + 9 lo g_{10} (y)) : - 4 - 9 lo g_{10} (y)

= lo g_{10} (x) - 4 - 9 lo g_{10} (y)

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

ln (2 e^{x^{2} + 2 x})

2 ln (x + 2) - 3 ln (x^{2} - 4) + ln (x - 2)

ln (\frac{5}{11})

What is expand log_{10}((sqrt(x))/(10000y^9)) ?
The solution to expand log_{10}((sqrt(x))/(10000y^9)) is log_{10}(sqrt(x))-4-9log_{10}(y)