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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

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) - 9 lo g_{10} (y)

\frac{1}{2 ln ( 2 )} + \frac{1}{3 ln ( 3 )}

ln (\frac{1}{( x - 1 ) ^{\frac{9}{2}}})

ln (48) - ln (3)

10 \cdot lo g_{10} (\frac{( 5 \cdot 1 0 ^{- 3} )}{1})

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