What is expand log_{3}(z^5sqrt(x)) ?

The solution to expand log_{3}(z^5sqrt(x)) is 5log_{3}(z)+log_{3}(sqrt(x))

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expand log_{3}(z^5sqrt(x))

expand

lo g_{3} (z^{5} x)

5 lo g_{3} (z) + lo g_{3} (x)

Solution steps

lo g_{3} (z^{5} x)

Apply log rule:

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

lo g_{3} (z^{5} x) = lo g_{3} (z^{5}) + lo g_{3} (x)

= lo g_{3} (z^{5}) + lo g_{3} (x)

Apply log rule:

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

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

= 5 lo g_{3} (z) + lo g_{3} (x)

lo g_{3} (\frac{4 ( x - 5 ) ^{2}}{x ^{4} ( x - 1 ) ^{3}})

ln (n) - ln (n + 1)

lo g_{6} (b) + 2 lo g_{6} (c) + \frac{lo g _{6} ( a )}{2}

6 ln (x) + 2 ln (y) - 3 ln (z)

What is expand log_{3}(z^5sqrt(x)) ?
The solution to expand log_{3}(z^5sqrt(x)) is 5log_{3}(z)+log_{3}(sqrt(x))