What is expand log_{10}(sqrt((y^5)/(x^5z))) ?

The solution to expand log_{10}(sqrt((y^5)/(x^5z))) is 1/2 (5log_{10}(y)-log_{10}(x^5z))

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expand log_{10}(sqrt((y^5)/(x^5z)))

expand

lo g_{10} (\frac{y ^{5}}{x ^{5} z})

\frac{1}{2} (5 lo g_{10} (y) - lo g_{10} (x^{5} z))

Solution steps

lo g_{10} (\frac{y ^{5}}{x ^{5} z})

Rewrite as

= lo g_{10} ((\frac{y ^{5}}{x ^{5} z})^{\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_{10} (\frac{y ^{5}}{x ^{5} z})

Simplify

lo g_{10} (\frac{y ^{5}}{x ^{5} z}) : 5 lo g_{10} (y) - lo g_{10} (x^{5} z)

= \frac{1}{2} (5 lo g_{10} (y) - lo g_{10} (x^{5} z))

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

= \frac{1}{2} (5 lo g_{10} (y) - (5 lo g_{10} (x) + lo g_{10} (z)))

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

= \frac{1}{2} (5 lo g_{10} (y) - lo g_{10} (x^{5} z))

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

= \frac{1}{2} (5 lo g_{10} (y) - (5 lo g_{10} (x) + lo g_{10} (z)))

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

= \frac{1}{2} (5 lo g_{10} (y) - lo g_{10} (x^{5} z))

\frac{2 ( 13 + y )}{3}

(\frac{6}{25}) \cdot (\frac{- 4}{5})

(m - 5)^{2}

2 a (6 b - 8)

(x + 1 + 3) (x + 1 - 3)

What is expand log_{10}(sqrt((y^5)/(x^5z))) ?
The solution to expand log_{10}(sqrt((y^5)/(x^5z))) is 1/2 (5log_{10}(y)-log_{10}(x^5z))