What is expand log_{10}(sqrt(xy^7)) ?

The solution to expand log_{10}(sqrt(xy^7)) is 3log_{10}(y)+1/2 log_{10}(xy)

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expand log_{10}(sqrt(xy^7))

expand

lo g_{10} (x y^{7})

3 lo g_{10} (y) + \frac{1}{2} lo g_{10} (x y)

Solution steps

lo g_{10} (x y^{7})

x y^{7} = y^{3} x y

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (x y) : \frac{1}{2} lo g_{10} (x y)

= lo g_{10} (y^{3}) + \frac{1}{2} lo g_{10} (x y)

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 3 lo g_{10} (y) + \frac{1}{2} lo g_{10} (x y)

\frac{1}{9} e^{2 x} (sin (3 x) + 2 cos (3 x) + c)

(t^{2} + e^{- t})^{2}

x (x + \frac{38400}{x ^{2}})

(x - 22) (x + 22) (x - 5) (x + 5) (x + 3)

5 + 16 + \frac{25}{4}

What is expand log_{10}(sqrt(xy^7)) ?
The solution to expand log_{10}(sqrt(xy^7)) is 3log_{10}(y)+1/2 log_{10}(xy)