What is 3log_{10}(2)+2log_{10}(3) ?

The solution to 3log_{10}(2)+2log_{10}(3) is log_{10}(72)

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simplify 3log_{10}(2)+2log_{10}(3)

simplify

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

lo g_{10} (72)

Decimal Notation

1.85733 \dots

Solution steps

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

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

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

2^{3} \cdot 3^{2} = 72

= lo g_{10} (72)

ln ((a b^{3})^{6})

2 ln (x + 4) - 7 ln (x)

lo g_{5} (25 x^{2})

lo g_{2} ((6 x)^{5})

5 lo g_{10} (a) + 25 lo g_{10} (b)

What is 3log_{10}(2)+2log_{10}(3) ?
The solution to 3log_{10}(2)+2log_{10}(3) is log_{10}(72)