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}((16y^2)/(x^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 y ^{2}}{x ^{2}})

Solution steps

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

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

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{3} (\frac{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})

Simplify

\frac{16}{x ^{2}} y^{2} : \frac{16 y ^{2}}{x ^{2}}

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

lo g_{e} (y \frac{y}{1 - y})

ln (4 \cdot 5)

lo g_{10} (x^{2} + 3 x + 2) - lo g_{10} (x + 1)

2 lo g_{3} (u) + 7 lo g_{3} (v)

lo g_{10} (\frac{c ^{3}}{a ^{2} b ^{3}})

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}((16y^2)/(x^2))