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

The solution to 2log_{3}(2)+log_{3}(5) is log_{3}(20)

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

simplify

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

lo g_{3} (20)

Decimal Notation

2.72683 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{2} \cdot 5 = 20

= lo g_{3} (20)

ln (\frac{x ^{2} + 5 x + 6}{( x + 3 ) ( x - 2 )})

9 ln (cos^{2} (t)) + 9 ln (1 + tan^{2} (t))

lo g_{3} (5) + lo g_{3} (8) - lo g_{3} (2)

lo g_{3} (9 x^{4})

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

What is 2log_{3}(2)+log_{3}(5) ?
The solution to 2log_{3}(2)+log_{3}(5) is log_{3}(20)