What is expand log_{3}((a^5b)/(c^2)) ?

The solution to expand log_{3}((a^5b)/(c^2)) is 5log_{3}(a)+log_{3}(b)-2log_{3}(c)

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expand log_{3}((a^5b)/(c^2))

expand

lo g_{3} (\frac{a ^{5} b}{c ^{2}})

5 lo g_{3} (a) + lo g_{3} (b) - 2 lo g_{3} (c)

Solution steps

lo g_{3} (\frac{a ^{5} b}{c ^{2}})

Apply log rule:

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

lo g_{3} (\frac{a ^{5} b}{c ^{2}}) = lo g_{3} (a^{5} b) - lo g_{3} (c^{2})

= lo g_{3} (a^{5} b) - lo g_{3} (c^{2})

Apply log rule:

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

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

= lo g_{3} (a^{5} b) - 2 lo g_{3} (c)

Apply log rule:

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

lo g_{3} (a^{5} b) = lo g_{3} (a^{5}) + lo g_{3} (b)

= lo g_{3} (a^{5}) + lo g_{3} (b) - 2 lo g_{3} (c)

Apply log rule:

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

lo g_{3} (a^{5}) = 5 lo g_{3} (a)

= 5 lo g_{3} (a) + lo g_{3} (b) - 2 lo g_{3} (c)

2 ln (5) - 2 ln (3)

lo g_{2} (x - 4) + 5 lo g_{2} (x + 1) - 3 lo g_{2} (x - 1)

ln (\frac{1}{64})

- ln (\frac{x ^{3}}{x ^{4} + c})

2 lo g_{2} (a) + 2 lo g_{2} (b) + 2 lo g_{2} (a + b)

What is expand log_{3}((a^5b)/(c^2)) ?
The solution to expand log_{3}((a^5b)/(c^2)) is 5log_{3}(a)+log_{3}(b)-2log_{3}(c)