What is expand ln(sqrt(8t)) ?

The solution to expand ln(sqrt(8t)) is 1/2 ln(t)+3/2 ln(2)

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expand ln(sqrt(8t))

expand

ln (8 t)

\frac{1}{2} ln (t) + \frac{3}{2} ln (2)

Solution steps

ln (8 t)

8 t = 22 t

= ln (22 t)

Apply log rule:

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

ln (22 t) = ln (2 t) + ln (2)

= ln (2 t) + ln (2)

Simplify

ln (2) : \frac{1}{2} ln (2)

= ln (2 t) + \frac{1}{2} ln (2)

ln (2 t) = ln (2) + \frac{1}{2} ln (t)

= ln (2) + \frac{1}{2} ln (t) + \frac{1}{2} ln (2)

Group like terms

= \frac{1}{2} ln (t) + ln (2) + \frac{1}{2} ln (2)

Add similar elements:

ln (2) + \frac{1}{2} ln (2) = \frac{3}{2} ln (2)

= \frac{1}{2} ln (t) + \frac{3}{2} ln (2)

(x - 3)^{2}

(1 + cot (x))^{2}

(csc (x) - cot (x)) (1 + cos (x))

\frac{( k + 1 ) ( k + 2 ) ( 2 k + 3 )}{6}

(1 + x^{\frac{2}{3}}) (1 - x^{\frac{2}{3}})

What is expand ln(sqrt(8t)) ?
The solution to expand ln(sqrt(8t)) is 1/2 ln(t)+3/2 ln(2)