What is expand log_{3}((sqrt(5))/(q^2p)) ?

The solution to expand log_{3}((sqrt(5))/(q^2p)) is 1/2 log_{3}(5)-2log_{3}(q)-log_{3}(p)

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expand log_{3}((sqrt(5))/(q^2p))

expand

lo g_{3} (\frac{5}{q ^{2} p})

\frac{1}{2} lo g_{3} (5) - 2 lo g_{3} (q) - lo g_{3} (p)

Solution steps

lo g_{3} (\frac{5}{q ^{2} p})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{3} (\frac{5}{q ^{2} p}) = lo g_{3} (5) - lo g_{3} (q^{2} p)

= lo g_{3} (5) - lo g_{3} (q^{2} p)

Apply log rule:

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

lo g_{3} (q^{2} p) = lo g_{3} (q^{2}) + lo g_{3} (p)

= lo g_{3} (5) - (lo g_{3} (q^{2}) + lo g_{3} (p))

Apply log rule:

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

lo g_{3} (q^{2}) = 2 lo g_{3} (q)

= lo g_{3} (5) - (2 lo g_{3} (q) + lo g_{3} (p))

lo g_{3} (5) = \frac{1}{2} lo g_{3} (5)

= \frac{1}{2} lo g_{3} (5) - (2 lo g_{3} (q) + lo g_{3} (p))

- (2 lo g_{3} (q) + lo g_{3} (p)) : - 2 lo g_{3} (q) - lo g_{3} (p)

= \frac{1}{2} lo g_{3} (5) - 2 lo g_{3} (q) - lo g_{3} (p)

ln (3 - x^{2}) - ln (x + 3)

ln (x^{2} - 13 x + 36) + 2 ln (x - 4) - ln (x - 9)

lo g_{b} (m^{3} n^{2} p^{5})

lo g_{8} (\frac{64}{x + 1})

lo g_{10} (\frac{x}{10 y ^{6}})

What is expand log_{3}((sqrt(5))/(q^2p)) ?
The solution to expand log_{3}((sqrt(5))/(q^2p)) is 1/2 log_{3}(5)-2log_{3}(q)-log_{3}(p)