What is expand ln(sqrt(2x)(x+3)^5) ?

The solution to expand ln(sqrt(2x)(x+3)^5) is ln(sqrt(2)sqrt(x))+5ln(x+3)

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expand ln(sqrt(2x)(x+3)^5)

expand

ln (2 x (x + 3)^{5})

ln (2 x) + 5 ln (x + 3)

Solution steps

ln (2 x (x + 3)^{5})

Apply log rule:

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

ln (2 x (x + 3)^{5}) = ln (2 x) + ln ((x + 3)^{5})

= ln (2 x) + ln ((x + 3)^{5})

Apply log rule:

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

ln ((x + 3)^{5}) = 5 ln (x + 3)

= ln (2 x) + 5 ln (x + 3)

2 x = 2 x

= ln (2 x) + 5 ln (x + 3)

2 lo g_{3} (x) + lo g_{3} (x - 3)

lo g_{10} (2) + lo g_{10} (18)

lo g_{10} (y^{8} z)

lo g_{3} (4) + 2 lo g_{3} (\frac{1}{2}) + lo g_{3} (x)

lo g_{10} (3 x + 1) - lo g_{10} (3 x^{2} - 5 x - 2)

What is expand ln(sqrt(2x)(x+3)^5) ?
The solution to expand ln(sqrt(2x)(x+3)^5) is ln(sqrt(2)sqrt(x))+5ln(x+3)