What is expand log_{4}(sqrt(6*11*5)) ?

The solution to expand log_{4}(sqrt(6*11*5)) is 1/2 log_{4}(330)

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expand log_{4}(sqrt(6115))

expand

lo g_{4} (6 \cdot 11 \cdot 5)

\frac{1}{2} lo g_{4} (330)

Decimal Notation

2.09158 \dots

Solution steps

lo g_{4} (6 \cdot 11 \cdot 5)

Rewrite as

= lo g_{4} ((6 \cdot 11 \cdot 5)^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} lo g_{4} (6 \cdot 11 \cdot 5)

Multiply the numbers:

6 \cdot 11 \cdot 5 = 330

= \frac{1}{2} lo g_{4} (330)

3 (3 + 5)

\frac{5}{s ^{4} ( s ^{2} + 36 )}

\frac{2 ( 8 + 19 )}{3}

\frac{N ( N + 1 ) ( N + 2 )}{6}

\frac{( s - 6 )}{( s + 2 ) ( s ^{2} + 9 )}

What is expand log_{4}(sqrt(6*11*5)) ?
The solution to expand log_{4}(sqrt(6*11*5)) is 1/2 log_{4}(330)