What is log_{10}(x)-2[log_{10}(y)+3log_{10}(z)] ?

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

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simplify log_{10}(x)-2[log_{10}(y)+3log_{10}(z)]

simplify

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

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

Solution steps

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

Apply log rule:

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

3 lo g_{10} (z) = lo g_{10} (z^{3})

= lo g_{10} (x) - 2 [lo g_{10} (y) + lo g_{10} (z^{3})]

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

= lo g_{10} (x) - 2 [lo g_{10} (y z^{3})]

Remove parentheses:

(a) = a

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

lo g_{6} (\frac{36}{x + 1})

ln (x \cdot e^{y})

lo g_{10} (\frac{y}{1})

ln (\frac{1 - 1 - 4 x ^{2}}{2 x})

- lo g_{10} (1.34 \cdot 1 0^{- 3})

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