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

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

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

simplify

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_{4} (7) + lo g_{4} (11)

lo g_{3} (27) + lo g_{10} (+ \frac{3}{4})

lo g_{7} (\frac{x ^{2}}{y ^{2} z ^{3}})

- lo g_{10} (3.25 \cdot 1 0^{- 6})

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