What is expand log_{m}(ab^2sqrt(c^3)) ?

The solution to expand log_{m}(ab^2sqrt(c^3)) is log_{m}(a)+2log_{m}(b)+log_{m}(sqrt(c)sqrt(c^2))

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expand log_{m}(ab^2sqrt(c^3))

expand

lo g_{m} (a b^{2} c^{3})

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

Solution steps

lo g_{m} (a b^{2} c^{3})

Apply log rule:

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

lo g_{m} (a b^{2} c^{3}) = lo g_{m} (a) + lo g_{m} (b^{2}) + lo g_{m} (c^{3})

= lo g_{m} (a) + lo g_{m} (b^{2}) + lo g_{m} (c^{3})

Apply log rule:

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

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

= lo g_{m} (a) + 2 lo g_{m} (b) + lo g_{m} (c^{3})

c^{3} = c c^{2}

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

- lo g_{10} (1.32 \cdot 1 0^{- 3})

lo g_{10} (10 a)

5 ln (x) - \frac{1}{5} ln (y)

- (\frac{2}{14}) lo g_{2} (\frac{2}{14}) - (\frac{3}{14}) lo g_{2} (\frac{3}{14})

lo g_{3} (\frac{9 x ^{4}}{y})

What is expand log_{m}(ab^2sqrt(c^3)) ?
The solution to expand log_{m}(ab^2sqrt(c^3)) is log_{m}(a)+2log_{m}(b)+log_{m}(sqrt(c)sqrt(c^2))