What is expand 20log_{10}(sqrt(x\sqrt{z)}) ?

The solution to expand 20log_{10}(sqrt(x\sqrt{z)}) is 5(log_{10}(z)+2log_{10}(x))

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expand 20log_{10}(sqrt(x\sqrt{z)})

expand

20 lo g_{10} (x z)

5 (lo g_{10} (z) + 2 lo g_{10} (x))

Solution steps

20 lo g_{10} (x z)

Simplify

lo g_{10} (x z) : \frac{1}{2} lo g_{10} (x z)

= 20 \cdot \frac{1}{2} lo g_{10} (x z)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 20}{2} lo g_{10} (x z)

Expand

\frac{1 \cdot 20}{2} : 10

= 10 lo g_{10} (x z)

Simplify

lo g_{10} (x z) : lo g_{10} (x) + \frac{1}{2} lo g_{10} (z)

= 10 (lo g_{10} (x) + \frac{1}{2} lo g_{10} (z))

Apply the distributive law:

a (b + c) = ab + a c

a = 10, b = lo g_{10} (x), c = \frac{1}{2} lo g_{10} (z)

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

Simplify

10 lo g_{10} (x) + 10 \cdot \frac{1}{2} lo g_{10} (z) : 5 (lo g_{10} (z) + 2 lo g_{10} (x))

= 5 (lo g_{10} (z) + 2 lo g_{10} (x))

(2 x - 1) x

\frac{x y ( x y + x ^{2} )}{x ^{4} + y ^{4}}

(x + 3 y) (x - 3 y)

\frac{x ^{4} ( x - 5 )}{100}

(t^{2} + 1) \cdot (t^{2} + 1)

What is expand 20log_{10}(sqrt(x\sqrt{z)}) ?
The solution to expand 20log_{10}(sqrt(x\sqrt{z)}) is 5(log_{10}(z)+2log_{10}(x))