What is expand log_{10}(7)(5y(3y+4)) ?

The solution to expand log_{10}(7)(5y(3y+4)) is 15log_{10}(7)y^2+20log_{10}(7)y

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expand log_{10}(7)(5y(3y+4))

expand

lo g_{10} (7) (5 y (3 y + 4))

15 lo g_{10} (7) y^{2} + 20 lo g_{10} (7) y

Solution steps

lo g_{10} (7) (5 y (3 y + 4))

Remove parentheses:

(a) = a

= lo g_{10} (7) \cdot 5 y (3 y + 4)

= 5 lo g_{10} (7) y (3 y + 4)

Apply the distributive law:

a (b + c) = ab + a c

a = lo g_{10} (7) \cdot 5 y, b = 3 y, c = 4

= lo g_{10} (7) \cdot 5 y \cdot 3 y + lo g_{10} (7) \cdot 5 y \cdot 4

= 5 \cdot 3 lo g_{10} (7) yy + 5 \cdot 4 lo g_{10} (7) y

Simplify

5 \cdot 3 lo g_{10} (7) yy + 5 \cdot 4 lo g_{10} (7) y : 15 lo g_{10} (7) y^{2} + 20 lo g_{10} (7) y

= 15 lo g_{10} (7) y^{2} + 20 lo g_{10} (7) y

\frac{2 ( - x ^{2} - 3 )}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

\frac{( - 2 x ^{2} + 18 )}{( x ^{2} + 9 ) ^{2}}

(x + y - 2) d x + (x - y + 4) d y

\frac{d}{d x} ((x - 1) (x - 5)^{3}) + 1

(y sin (x) + cos^{2} (x)) d x

What is expand log_{10}(7)(5y(3y+4)) ?
The solution to expand log_{10}(7)(5y(3y+4)) is 15log_{10}(7)y^2+20log_{10}(7)y