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

The solution to 2log_{10}(3)+log_{10}(5) is log_{10}(45)

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

simplify

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

lo g_{10} (45)

Decimal Notation

1.65321 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} \cdot 5 = 45

= lo g_{10} (45)

lo g_{10} (p) - 3 lo g_{10} (q) - \frac{1}{2} lo g_{10} (n)

lo g_{10} \frac{m}{( \frac{p}{q} )}

20 ln (\frac{1400}{1400 + 100 ( 30 )}) + 9.8 (30)

8 lo g_{3} (x) - 2 lo g_{3} (z) - 7 lo g_{3} (y)

\frac{1}{4} ln (1296) - ln (2)

What is 2log_{10}(3)+log_{10}(5) ?
The solution to 2log_{10}(3)+log_{10}(5) is log_{10}(45)