What is log_{4}(16x^4y^3) ?

The solution to log_{4}(16x^4y^3) is 2+4log_{4}(x)+3log_{4}(y)

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simplify log_{4}(16x^4y^3)

simplify

lo g_{4} (16 x^{4} y^{3})

2 + 4 lo g_{4} (x) + 3 lo g_{4} (y)

Solution steps

lo g_{4} (16 x^{4} y^{3})

Factor the number:

16 = 4^{2}

= lo g_{4} (4^{2} x^{4} y^{3})

Apply log rule:

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

lo g_{4} (4^{2} x^{4} y^{3}) = lo g_{4} (4^{2}) + lo g_{4} (x^{4} y^{3})

= lo g_{4} (4^{2}) + lo g_{4} (x^{4} y^{3})

Apply log rule:

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

lo g_{4} (4^{2}) = 2

= 2 + lo g_{4} (x^{4} y^{3})

Simplify

lo g_{4} (x^{4} y^{3}) : 4 lo g_{4} (x) + 3 lo g_{4} (y)

= 2 + (4 lo g_{4} (x) + 3 lo g_{4} (y))

Apply rule:

a + (b + c) = a + b + c

2 + (4 lo g_{4} (x) + 3 lo g_{4} (y)) = 2 + 4 lo g_{4} (x) + 3 lo g_{4} (y)

= 2 + 4 lo g_{4} (x) + 3 lo g_{4} (y)

(2 x (x^{2} + 1)^{\frac{1}{2}})^{2}

\frac{2}{3} + \frac{1}{4} + \frac{1}{18}

tan^{2} (2 x) - sec^{2} (x)

\frac{( 18 n ^{2} - 9 n + 1 )}{( 3 n - 1 )}

\frac{csc ( x )}{sec ( x )}

What is log_{4}(16x^4y^3) ?
The solution to log_{4}(16x^4y^3) is 2+4log_{4}(x)+3log_{4}(y)