What is log_{10}(10000x^4y^6) ?

The solution to log_{10}(10000x^4y^6) is 4+4log_{10}(x)+6log_{10}(y)

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simplify log_{10}(10000x^4y^6)

simplify

lo g_{10} (10000 x^{4} y^{6})

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

Solution steps

lo g_{10} (10000 x^{4} y^{6})

Factor the number:

10000 = 1 0^{4}

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

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

Apply log rule:

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

lo g_{10} (1 0^{4}) = 4

= 4 + 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)

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

Apply rule:

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

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

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

lo g_{x} (\frac{x}{64})

lo g_{b} (\frac{x y ^{4}}{z ^{4}})

lo g_{a} (x yz)

5 ln ∣ cot (t) ∣ + 5 ln (1 + tan (2) (t))

What is log_{10}(10000x^4y^6) ?
The solution to log_{10}(10000x^4y^6) is 4+4log_{10}(x)+6log_{10}(y)