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

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

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

simplify

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

lo g_{10} (200)

Decimal Notation

2.30102 \dots

Solution steps

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

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

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

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

Apply log rule:

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

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

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

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

= lo g_{10} (200)

lo g_{3} (\frac{x}{a ^{3}})

- \frac{2}{7} lo g_{2} (\frac{2}{7}) - \frac{5}{7} lo g_{2} (\frac{5}{7})

lo g_{10} (1.86 \cdot 1 0^{6}) - lo g_{10} (6.9 \cdot 1 0^{4})

6.1 + lo g_{10} (\frac{24.6}{0.0308})

- ln (k C A CB)

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