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

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

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

simplify

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

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

Solution steps

\frac{3}{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})

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

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

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

Apply log rule:

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

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

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

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

lo g_{3} (\frac{1}{6})

\frac{ln ( m + Δ m ) - ln ( m - Δ m )}{2}

\frac{1}{2} ln (9 x^{2}) + ln (3 x)

ln (\frac{( 2 x + 3 ) ( x + 6 ) ^{4}}{( 1 - 4 x ) ^{5}})

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