What is expand log_{4}(3sqrt(2*5)) ?

The solution to expand log_{4}(3sqrt(2*5)) is log_{4}(3)+1/2 log_{4}(10)

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expand log_{4}(3sqrt(2*5))

expand

lo g_{4} (3 2 \cdot 5)

lo g_{4} (3) + \frac{1}{2} lo g_{4} (10)

Decimal Notation

1.62296 \dots

Solution steps

lo g_{4} (3 2 \cdot 5)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{4} (3 2 \cdot 5) = lo g_{4} (3) + lo g_{4} (2 \cdot 5)

= lo g_{4} (3) + lo g_{4} (2 \cdot 5)

lo g_{4} (2 \cdot 5) = \frac{1}{2} lo g_{4} (10)

= lo g_{4} (3) + \frac{1}{2} lo g_{4} (10)

(\frac{1}{3} ln ∣ e^{x} + 1 ∣ - \frac{1}{3} ln ∣ e^{x} - 2 ∣) \cdot e^{2 x}

lo g_{4} (32)

\frac{1}{2} ln (\frac{11}{5})

ln (- 6 \frac{e ^{(x)}}{3})

ln (1^{2} (1 + 2)^{\frac{9}{5}} (1 - 3)^{\frac{1}{5}})

What is expand log_{4}(3sqrt(2*5)) ?
The solution to expand log_{4}(3sqrt(2*5)) is log_{4}(3)+1/2 log_{4}(10)