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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

= 2 + lo g_{10} (x^{2}) - \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}})

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

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

ln (\frac{1}{- x})

ln (\frac{1.5 \cdot 1 0 ^{4}}{1.5 \cdot 1 0 ^{10}})

\frac{( ln ( 0.25 ) + ln ( 0.5 ) + ln ( 0.75 ) ) \cdot 2 \cdot 0.5}{2}

(\frac{3}{2})^{2} \cdot ln (\frac{3}{2})

lo g_{b} (5) + 2 lo g_{b} (2)

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