What is 17/3 log_{10}(x)-3/2 log_{10}(y) ?

The solution to 17/3 log_{10}(x)-3/2 log_{10}(y) is log_{10}((x^{17/3})/(y^{3/2)})

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simplify 17/3 log_{10}(x)-3/2 log_{10}(y)

simplify

\frac{17}{3} lo g_{10} (x) - \frac{3}{2} lo g_{10} (y)

lo g_{10} (\frac{x ^{\frac{17}{3}}}{y ^{\frac{3}{2}}})

Solution steps

\frac{17}{3} lo g_{10} (x) - \frac{3}{2} lo g_{10} (y)

Apply log rule:

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

\frac{17}{3} lo g_{10} (x) = lo g_{10} (x^{\frac{17}{3}})

= lo g_{10} (x^{\frac{17}{3}}) - \frac{3}{2} lo g_{10} (y)

Apply log rule:

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

\frac{3}{2} lo g_{10} (y) = lo g_{10} (y^{\frac{3}{2}})

= lo g_{10} (x^{\frac{17}{3}}) - lo g_{10} (y^{\frac{3}{2}})

Apply log rule:

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

lo g_{10} (x^{\frac{17}{3}}) - lo g_{10} (y^{\frac{3}{2}}) = lo g_{10} (\frac{x ^{\frac{17}{3}}}{y ^{\frac{3}{2}}})

= lo g_{10} (\frac{x ^{\frac{17}{3}}}{y ^{\frac{3}{2}}})

lo g_{9} (8)

0.75 \cdot ln (10000) + 0.25 \cdot ln (9000)

0 - \frac{0.025693}{2} ln (\frac{3}{2.4 \cdot 1 0 ^{- 3}})

ln (\frac{x ^{2} cos ( x )}{1 + x})

2 - \frac{1}{2} lo g_{10} (x) - 2 lo g_{10} (y)

What is 17/3 log_{10}(x)-3/2 log_{10}(y) ?
The solution to 17/3 log_{10}(x)-3/2 log_{10}(y) is log_{10}((x^{17/3})/(y^{3/2)})