What is log_{2}(45)-log_{2}(5) ?

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

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simplify log_{2}(45)-log_{2}(5)

simplify

lo g_{2} (45) - lo g_{2} (5)

2 lo g_{2} (3)

Decimal Notation

3.16992 \dots

Solution steps

lo g_{2} (45) - lo g_{2} (5)

Apply log rule:

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

lo g_{2} (45) - lo g_{2} (5) = lo g_{2} (\frac{45}{5})

= lo g_{2} (\frac{45}{5})

Divide the numbers:

\frac{45}{5} = 9

= lo g_{2} (9)

Factor the number:

9 = 3^{2}

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

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

= 2 lo g_{2} (3)

lo g_{2} (\frac{x ^{3} y}{5 z ^{6}})

- 4 lo g_{b} (d) + lo g_{b} (e) - 2 lo g_{b} (f)

lo g_{10} (\frac{3 x}{y})

ln ∣ b ∣ - ln ∣ a ∣

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