What is log_{4}(20)-log_{4}(45)+log_{4}(144) ?

The solution to log_{4}(20)-log_{4}(45)+log_{4}(144) is 3

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simplify log_{4}(20)-log_{4}(45)+log_{4}(144)

simplify

lo g_{4} (20) - lo g_{4} (45) + lo g_{4} (144)

3

Solution steps

lo g_{4} (20) - lo g_{4} (45) + lo g_{4} (144)

Apply log rule:

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

lo g_{4} (20) - lo g_{4} (45) = lo g_{4} (\frac{20}{45})

= lo g_{4} (\frac{20}{45}) + lo g_{4} (144)

Apply log rule:

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

lo g_{4} (\frac{20}{45}) + lo g_{4} (144) = lo g_{4} (\frac{20}{45} \cdot 144)

= lo g_{4} (\frac{20}{45} \cdot 144)

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (\frac{20}{45} \cdot 144)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{2}} (\frac{20}{45} \cdot 144) = \frac{1}{2} lo g_{2} (\frac{20}{45} \cdot 144)

= \frac{1}{2} lo g_{2} (\frac{20}{45} \cdot 144)

\frac{20}{45} \cdot 144 = 64

= \frac{1}{2} lo g_{2} (64)

Factor the number:

64 = 2^{6}

= \frac{1}{2} lo g_{2} (2^{6})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{2} (2^{6}) = 6

= \frac{1}{2} \cdot 6

\frac{1}{2} \cdot 6 = 3

= 3

2 (- 1)^{2} + 3 (- 1) + C = 1

- \frac{1}{4} - \frac{7}{8}

2 x^{3} + 7 x^{2} + 12 x + 9

- 1 < 3 x - 5 \leq 6

27 a^{3} + b^{6}

What is log_{4}(20)-log_{4}(45)+log_{4}(144) ?
The solution to log_{4}(20)-log_{4}(45)+log_{4}(144) is 3