What is log_{10}(8x^2yz) ?

The solution to log_{10}(8x^2yz) is 3log_{10}(2)+2log_{10}(x)+log_{10}(y)+log_{10}(z)

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simplify log_{10}(8x^2yz)

simplify

lo g_{10} (8 x^{2} yz)

3 lo g_{10} (2) + 2 lo g_{10} (x) + lo g_{10} (y) + lo g_{10} (z)

Solution steps

lo g_{10} (8 x^{2} yz)

Apply log rule:

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

lo g_{10} (8 x^{2} yz) = lo g_{10} (8) + lo g_{10} (x^{2}) + lo g_{10} (y) + lo g_{10} (z)

= lo g_{10} (8) + lo g_{10} (x^{2}) + lo g_{10} (y) + lo g_{10} (z)

lo g_{10} (8) = 3 lo g_{10} (2)

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

= 3 lo g_{10} (2) + 2 lo g_{10} (x) + lo g_{10} (y) + lo g_{10} (z)

lo g_{10} (\frac{3 x ^{2}}{2})

- ln (\frac{e ^{2} - 1}{2 e ^{2}})

lo g_{2} (A) + lo g_{2} (B)

lo g_{10} (\frac{z ^{3} y}{x ^{4}})

ln (2) + ln (x) - ln (x - 1)

What is log_{10}(8x^2yz) ?
The solution to log_{10}(8x^2yz) is 3log_{10}(2)+2log_{10}(x)+log_{10}(y)+log_{10}(z)