What is log_{4}(20)+log_{4}(5) ?

The solution to log_{4}(20)+log_{4}(5) is log_{2}(10)

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simplify log_{4}(20)+log_{4}(5)

simplify

lo g_{4} (20) + lo g_{4} (5)

lo g_{2} (10)

Decimal Notation

3.32192 \dots

Solution steps

lo g_{4} (20) + lo g_{4} (5)

Apply log rule:

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

lo g_{4} (20) + lo g_{4} (5) = lo g_{4} (20 \cdot 5)

= lo g_{4} (20 \cdot 5)

Multiply the numbers:

20 \cdot 5 = 100

= lo g_{4} (100)

Factor the number:

100 = 1 0^{2}

= lo g_{4} (1 0^{2})

Apply log rule:

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

lo g_{4} (1 0^{2}) = 2 lo g_{4} (10)

= 2 lo g_{4} (10)

Factor the number:

4 = 2^{2}

= 2 lo g_{2^{2}} (10)

Apply log rule:

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

lo g_{2^{2}} (10) = \frac{1}{2} lo g_{2} (10)

= 2 \cdot \frac{1}{2} lo g_{2} (10)

2 \cdot \frac{1}{2} lo g_{2} (10) = lo g_{2} (10)

= lo g_{2} (10)

lo g_{10} (\frac{365}{2.4}) + 2.8

2 ln (x - 4) - 9 ln (x)

lo g_{10} (\frac{y}{1000})

lo g_{7} (x^{5}) - 5 lo g_{7} (x^{2})

lo g_{5} (\frac{9 x}{y ^{3}})

What is log_{4}(20)+log_{4}(5) ?
The solution to log_{4}(20)+log_{4}(5) is log_{2}(10)