What is expand log_{7}(sqrt(49x^5)) ?

The solution to expand log_{7}(sqrt(49x^5)) is 5/2 log_{7}(x)+1

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expand log_{7}(sqrt(49x^5))

expand

lo g_{7} (49 x^{5})

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

Solution steps

lo g_{7} (49 x^{5})

49 x^{5} = 7 x^{2} x

= lo g_{7} (7 x^{2} x)

Apply log rule:

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

lo g_{7} (7 x^{2} x) = lo g_{7} (x^{2} x) + lo g_{7} (7)

= lo g_{7} (x^{2} x) + lo g_{7} (7)

Simplify

lo g_{7} (7) : 1

Apply log rule:

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

lo g_{7} (x^{2} x) = lo g_{7} (x) + lo g_{7} (x^{2})

= lo g_{7} (x) + lo g_{7} (x^{2}) + 1

Apply log rule:

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

lo g_{7} (x) + lo g_{7} (x^{2}) = lo g_{7} (x^{2} x)

= lo g_{7} (x x^{2}) + 1

lo g_{7} (x x^{2}) = \frac{5}{2} lo g_{7} (x)

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

\frac{1}{( 1 + x ) ^{8}}

2 ((4 - t^{6}) (- 2 + t^{6}))

e^{2 x} (2 e^{2 x} x^{2} + 2 e^{2 x} x + e^{2 x})

(2 x y^{3} + 4) d x + (3 x^{2} y^{2} + 8) d y

sin (2 (x - π))

What is expand log_{7}(sqrt(49x^5)) ?
The solution to expand log_{7}(sqrt(49x^5)) is 5/2 log_{7}(x)+1