What is log_{3}(16)+2*log_{3}(x)-2*log_{3}(y) ?

The solution to log_{3}(16)+2*log_{3}(x)-2*log_{3}(y) is log_{3}((16x^2)/(y^2))

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simplify log_{3}(16)+2log_{3}(x)-2log_{3}(y)

simplify

lo g_{3} (16) + 2 \cdot lo g_{3} (x) - 2 \cdot lo g_{3} (y)

lo g_{3} (\frac{16 x ^{2}}{y ^{2}})

Solution steps

lo g_{3} (16) + 2 lo g_{3} (x) - 2 lo g_{3} (y)

Apply log rule:

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

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

= lo g_{3} (16) + lo g_{3} (x^{2}) - 2 lo g_{3} (y)

Apply log rule:

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

lo g_{3} (16) + lo g_{3} (x^{2}) = lo g_{3} (16 x^{2})

= lo g_{3} (16 x^{2}) - 2 lo g_{3} (y)

Apply log rule:

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

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

= lo g_{3} (16 x^{2}) - lo g_{3} (y^{2})

Apply log rule:

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

lo g_{3} (16 x^{2}) - lo g_{3} (y^{2}) = lo g_{3} (\frac{16 x ^{2}}{y ^{2}})

= lo g_{3} (\frac{16 x ^{2}}{y ^{2}})

ln (x (x + 7))

lo g_{6} (z^{4} x)

lo g_{10} (\frac{5 b}{4})

lo g_{5} (z^{2} x)

What is log_{3}(16)+2*log_{3}(x)-2*log_{3}(y) ?
The solution to log_{3}(16)+2*log_{3}(x)-2*log_{3}(y) is log_{3}((16x^2)/(y^2))