What is log_{10}(1000x^3y^5) ?

The solution to log_{10}(1000x^3y^5) is 3+3log_{10}(x)+5log_{10}(y)

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simplify log_{10}(1000x^3y^5)

simplify

lo g_{10} (1000 x^{3} y^{5})

3 + 3 lo g_{10} (x) + 5 lo g_{10} (y)

Solution steps

lo g_{10} (1000 x^{3} y^{5})

Factor the number:

1000 = 1 0^{3}

= lo g_{10} (1 0^{3} x^{3} y^{5})

Apply log rule:

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

lo g_{10} (1 0^{3} x^{3} y^{5}) = lo g_{10} (1 0^{3}) + lo g_{10} (x^{3} y^{5})

= lo g_{10} (1 0^{3}) + lo g_{10} (x^{3} y^{5})

Apply log rule:

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

lo g_{10} (1 0^{3}) = 3

= 3 + lo g_{10} (x^{3} y^{5})

Simplify

lo g_{10} (x^{3} y^{5}) : 3 lo g_{10} (x) + 5 lo g_{10} (y)

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

Apply rule:

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

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

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

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

ln (\frac{9}{2})

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

7 ln (x) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

3 lo g_{5} (2) + lo g_{5} (7)

What is log_{10}(1000x^3y^5) ?
The solution to log_{10}(1000x^3y^5) is 3+3log_{10}(x)+5log_{10}(y)