What is 3log_{10}(2)+2log_{10}(5) ?

The solution to 3log_{10}(2)+2log_{10}(5) is log_{10}(200)

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simplify 3log_{10}(2)+2log_{10}(5)

simplify

3 lo g_{10} (2) + 2 lo g_{10} (5)

lo g_{10} (200)

Decimal Notation

2.30102 \dots

Solution steps

3 lo g_{10} (2) + 2 lo g_{10} (5)

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

2 lo g_{10} (5) = lo g_{10} (5^{2})

= lo g_{10} (2^{3}) + lo g_{10} (5^{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} (5^{2}) = lo g_{10} (2^{3} \cdot 5^{2})

= lo g_{10} (2^{3} \cdot 5^{2})

2^{3} \cdot 5^{2} = 200

= lo g_{10} (200)

ln (3.61 \cdot 1 0^{- 11})

lo g_{10} (\frac{x ^{15} y ^{17}}{z ^{13}})

ln (x (x + 1) (x + 2))

lo g_{6} (72) - lo g_{6} (144) - lo g_{6} (18)

(lo g_{b} (x) - lo g_{b} (y)) + 6 lo g_{b} (v)

What is 3log_{10}(2)+2log_{10}(5) ?
The solution to 3log_{10}(2)+2log_{10}(5) is log_{10}(200)