What is expand log_{10}(ab^2sqrt(c)) ?

The solution to expand log_{10}(ab^2sqrt(c)) is log_{10}(a)+2log_{10}(b)+log_{10}(sqrt(c))

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expand log_{10}(ab^2sqrt(c))

expand

lo g_{10} (a b^{2} c)

lo g_{10} (a) + 2 lo g_{10} (b) + lo g_{10} (c)

Solution steps

lo g_{10} (a b^{2} c)

Apply log rule:

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

lo g_{10} (a b^{2} c) = lo g_{10} (a) + lo g_{10} (b^{2}) + lo g_{10} (c)

= lo g_{10} (a) + lo g_{10} (b^{2}) + lo g_{10} (c)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{10} (a) + 2 lo g_{10} (b) + lo g_{10} (c)

ln (x e^{(\frac{y}{z})})

- \frac{ln ( \frac{9}{2} ) - ln ( \frac{25}{2} )}{4}

- lo g_{10} (1.4 \cdot 1 0^{- 6})

\frac{20}{100} \cdot ln (\frac{20}{100})

lo g_{3} (3 x^{3} y^{5})

What is expand log_{10}(ab^2sqrt(c)) ?
The solution to expand log_{10}(ab^2sqrt(c)) is log_{10}(a)+2log_{10}(b)+log_{10}(sqrt(c))