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

The solution to log_{2}(3)+2log_{2}(5) is log_{2}(75)

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

simplify

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

lo g_{2} (75)

Decimal Notation

6.22881 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 \cdot 5^{2} = 75

= lo g_{2} (75)

ln (- 3 y)

- lo g_{10} (3 \cdot 1 0^{- 6})

- lo g_{10} (7.5 \times 1 0^{- 6})

lo g_{e} (3 x)

lo g_{4} (x^{7}) - lo g_{4} (x^{2}) + 4 lo g_{4} (x^{3})

What is log_{2}(3)+2log_{2}(5) ?
The solution to log_{2}(3)+2log_{2}(5) is log_{2}(75)