What is expand log_{5}(sqrt(ab^7)) ?

The solution to expand log_{5}(sqrt(ab^7)) is 3log_{5}(b)+1/2 log_{5}(ab)

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expand log_{5}(sqrt(ab^7))

expand

lo g_{5} (a b^{7})

3 lo g_{5} (b) + \frac{1}{2} lo g_{5} (ab)

Solution steps

lo g_{5} (a b^{7})

a b^{7} = b^{3} ab

= lo g_{5} (b^{3} ab)

Apply log rule:

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

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

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

Apply log rule:

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

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

= lo g_{5} (ab b^{3})

Apply log rule:

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

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

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

Simplify

lo g_{5} (ab) : \frac{1}{2} lo g_{5} (ab)

= lo g_{5} (b^{3}) + \frac{1}{2} lo g_{5} (ab)

Apply log rule

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

assuming

x \geq 0

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

x (x + 1) (2 x - 1)

(- sec (x) - cos (x)) cos (x)

(1 - x + x^{2}) (5 + x)

(2 + i)^{4}

f (2 u + v, v - u)

What is expand log_{5}(sqrt(ab^7)) ?
The solution to expand log_{5}(sqrt(ab^7)) is 3log_{5}(b)+1/2 log_{5}(ab)