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

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

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

simplify

2 lo g_{2} (x) + 3 lo g_{2} (y)

lo g_{2} (x^{2} y^{3})

Solution steps

2 lo g_{2} (x) + 3 lo g_{2} (y)

Apply log rule:

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

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

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

Apply log rule:

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

3 lo g_{2} (y) = lo g_{2} (y^{3})

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

Apply log rule:

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

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

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

ln (x^{2} - 1) - ln (x + 1)

\frac{7}{4} ln (x) - \frac{5}{4} ln (y) - \frac{1}{4} ln (z) + \frac{1}{4} ln (x)

ln (\frac{2}{e})

lo g_{5} (\frac{x ^{2} y}{z ^{3}})

lo g_{10} (\frac{x ^{2}}{y ^{4}})

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