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

The solution to 3log_{10}(2)+log_{10}(3) is log_{10}(24)

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

simplify

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

lo g_{10} (24)

Decimal Notation

1.38021 \dots

Solution steps

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

Apply log rule:

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

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

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

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

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

2^{3} \cdot 3 = 24

= lo g_{10} (24)

lo g_{10} (6) - lo g_{10} (5)

lo g_{10} (\frac{π}{6})

lo g_{2} (7) - lo g_{2} (11)

lo g_{4} (\frac{4 x ^{8}}{y})

lo g_{3} (\frac{x ^{4}}{x + 1})

What is 3log_{10}(2)+log_{10}(3) ?
The solution to 3log_{10}(2)+log_{10}(3) is log_{10}(24)