What is expand log_{3}(sqrt(5a^7)) ?

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

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expand log_{3}(sqrt(5a^7))

expand

lo g_{3} (5 a^{7})

\frac{7}{2} lo g_{3} (a) + \frac{1}{2} lo g_{3} (5)

Solution steps

lo g_{3} (5 a^{7})

5 a^{7} = 5 a^{3} a

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{3} (a^{3} a) = \frac{7}{2} lo g_{3} (a)

= \frac{7}{2} lo g_{3} (a) + \frac{1}{2} lo g_{3} (5)

\frac{x ( 1 + x )}{( 1 - x ) ^{3}}

\frac{3}{( x - 1 ) ( x - 4 )}

e^{(t (t + 3))}

(5 + e^{i t})^{3}

(x - 3 i) (x - 2) (x + i)

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