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

The solution to 3log_{2}(5)+log_{2}(3) is log_{2}(375)

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

simplify

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

lo g_{2} (375)

Decimal Notation

8.55074 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5^{3} \cdot 3 = 375

= lo g_{2} (375)

lo g_{\frac{1}{4}} (16 z (x^{3} - 27))

- \frac{2}{3} lo g_{2} (\frac{2}{3}) - \frac{1}{3} lo g_{2} (\frac{1}{3})

2 (lo g_{5} (x) + 2 lo g_{5} (y) - 3 lo g_{5} (z))

lo g_{b} (2 x)

lo g_{2} (A) + lo g_{2} (B) - 2 lo g_{2} (C)

What is 3log_{2}(5)+log_{2}(3) ?
The solution to 3log_{2}(5)+log_{2}(3) is log_{2}(375)