What is 3log_{2}(5)-log_{2}(3)+log_{2}(6) ?

The solution to 3log_{2}(5)-log_{2}(3)+log_{2}(6) is log_{2}(250)

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simplify 3log_{2}(5)-log_{2}(3)+log_{2}(6)

simplify

3 lo g_{2} (5) - lo g_{2} (3) + lo g_{2} (6)

lo g_{2} (250)

Decimal Notation

7.96578 \dots

Solution steps

3 lo g_{2} (5) - lo g_{2} (3) + lo g_{2} (6)

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) + lo g_{2} (6)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

= lo g_{2} (\frac{5 ^{3}}{3}) + lo g_{2} (6)

Apply log rule:

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

lo g_{2} (\frac{5 ^{3}}{3}) + lo g_{2} (6) = lo g_{2} (\frac{5 ^{3}}{3} \cdot 6)

= lo g_{2} (\frac{5 ^{3}}{3} \cdot 6)

\frac{5 ^{3}}{3} \cdot 6 = 250

= lo g_{2} (250)

\frac{1}{3} (6 ln (x + 4) + ln (x) - ln (x^{2} - 8))

\frac{ln ( \frac{3}{2} )}{8 ln ( 10 )}

lo g_{2} (x^{2}) - lo g_{2} (x)

ln (\frac{k + 1}{k})

2 lo g_{10} (4 x) - lo g_{10} (8)

What is 3log_{2}(5)-log_{2}(3)+log_{2}(6) ?
The solution to 3log_{2}(5)-log_{2}(3)+log_{2}(6) is log_{2}(250)