What is expand log_{10}(3*2^3) ?

The solution to expand log_{10}(3*2^3) is log_{10}(3)+3log_{10}(2)

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expand log_{10}(3*2^3)

expand

lo g_{10} (3 \cdot 2^{3})

lo g_{10} (3) + 3 lo g_{10} (2)

Decimal Notation

1.38021 \dots

Solution steps

lo g_{10} (3 \cdot 2^{3})

Apply log rule:

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

lo g_{10} (3 \cdot 2^{3}) = lo g_{10} (3) + lo g_{10} (2^{3})

= lo g_{10} (3) + lo g_{10} (2^{3})

Apply log rule:

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

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

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

\frac{1}{2} lo g_{c} (x) + 4 lo g_{c} (y) - 3 lo g_{c} (x)

ln (12 x)

lo g_{b} (9) + 3 lo g_{b} (2)

\frac{1}{4} lo g_{c} (x) + 3 lo g_{c} (y) - 2 lo g_{c} (x)

ln (x e^{- x})

What is expand log_{10}(3*2^3) ?
The solution to expand log_{10}(3*2^3) is log_{10}(3)+3log_{10}(2)