What is log_{10}(1000x^4y^6) ?

The solution to log_{10}(1000x^4y^6) is 3+4log_{10}(x)+6log_{10}(y)

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simplify log_{10}(1000x^4y^6)

simplify

lo g_{10} (1000 x^{4} y^{6})

3 + 4 lo g_{10} (x) + 6 lo g_{10} (y)

Solution steps

lo g_{10} (1000 x^{4} y^{6})

Factor the number:

1000 = 1 0^{3}

= lo g_{10} (1 0^{3} x^{4} y^{6})

Apply log rule:

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

lo g_{10} (1 0^{3} x^{4} y^{6}) = lo g_{10} (1 0^{3}) + lo g_{10} (x^{4} y^{6})

= lo g_{10} (1 0^{3}) + lo g_{10} (x^{4} y^{6})

Apply log rule:

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

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

= 3 + lo g_{10} (x^{4} y^{6})

Simplify

lo g_{10} (x^{4} y^{6}) : 4 lo g_{10} (x) + 6 lo g_{10} (y)

= 3 + (4 lo g_{10} (x) + 6 lo g_{10} (y))

Apply rule:

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

3 + (4 lo g_{10} (x) + 6 lo g_{10} (y)) = 3 + 4 lo g_{10} (x) + 6 lo g_{10} (y)

= 3 + 4 lo g_{10} (x) + 6 lo g_{10} (y)

1 + lo g_{10} (Q) + lo g_{10} (2)

lo g_{c} (\frac{x ^{\frac{1}{2}} y ^{3}}{x ^{4}})

\frac{1}{4} lo g_{b} (x) + 3 lo g_{b} (y) - 5 lo g_{b} (x)

2 ln (x) - \frac{1}{3} ln (y) + 4 ln (z)

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

What is log_{10}(1000x^4y^6) ?
The solution to log_{10}(1000x^4y^6) is 3+4log_{10}(x)+6log_{10}(y)