What is log_{10}(100y^7z^{10}) ?

The solution to log_{10}(100y^7z^{10}) is 2+7log_{10}(y)+10log_{10}(z)

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simplify log_{10}(100y^7z^{10})

simplify

lo g_{10} (100 y^{7} z^{10})

2 + 7 lo g_{10} (y) + 10 lo g_{10} (z)

Solution steps

lo g_{10} (100 y^{7} z^{10})

Factor the number:

100 = 1 0^{2}

= lo g_{10} (1 0^{2} y^{7} z^{10})

Apply log rule:

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

lo g_{10} (1 0^{2} y^{7} z^{10}) = lo g_{10} (1 0^{2}) + lo g_{10} (y^{7} z^{10})

= lo g_{10} (1 0^{2}) + lo g_{10} (y^{7} z^{10})

Apply log rule:

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

lo g_{10} (1 0^{2}) = 2

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

Simplify

lo g_{10} (y^{7} z^{10}) : 7 lo g_{10} (y) + 10 lo g_{10} (z)

= 2 + (7 lo g_{10} (y) + 10 lo g_{10} (z))

Apply rule:

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

2 + (7 lo g_{10} (y) + 10 lo g_{10} (z)) = 2 + 7 lo g_{10} (y) + 10 lo g_{10} (z)

= 2 + 7 lo g_{10} (y) + 10 lo g_{10} (z)

ln (x x^{2} - 1)

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lo g_{9} (9 x)

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 5 lo g_{10} (z)

ln (5) + 2 ln (x) + 3 ln (x^{2} + 5)

What is log_{10}(100y^7z^{10}) ?
The solution to log_{10}(100y^7z^{10}) is 2+7log_{10}(y)+10log_{10}(z)