What is 2ln(2)+5ln(x)-1/2 ln(x+3) ?

The solution to 2ln(2)+5ln(x)-1/2 ln(x+3) is ln((4x^5sqrt(x+3))/(x+3))

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simplify 2ln(2)+5ln(x)-1/2 ln(x+3)

simplify

2 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 3)

ln (\frac{4 x ^{5} x + 3}{x + 3})

Solution steps

2 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (2) = ln (2^{2})

= ln (2^{2}) + 5 ln (x) - \frac{1}{2} ln (x + 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (2^{2}) + ln (x^{5}) - \frac{1}{2} ln (x + 3)

Apply log rule:

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

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

= ln (2^{2} x^{5}) - \frac{1}{2} ln (x + 3)

2^{2} = 4

= ln (4 x^{5}) - \frac{1}{2} ln (x + 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (4 x^{5}) - ln ((x + 3)^{\frac{1}{2}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (4 x^{5}) - ln ((x + 3)^{\frac{1}{2}}) = ln (\frac{4 x ^{5}}{( x + 3 ) ^{\frac{1}{2}}})

= ln (\frac{4 x ^{5}}{( x + 3 ) ^{\frac{1}{2}}})

Simplify

\frac{4 x ^{5}}{( x + 3 ) ^{\frac{1}{2}}} : \frac{4 x ^{5} x + 3}{x + 3}

= ln (\frac{4 x ^{5} x + 3}{x + 3})

\frac{ln ( 2 i ) - ln ( 2 )}{2}

ln (P) - ln (- P + 1)

\frac{ln ( 2 )}{3 ln ( 2 ) - 2 ln ( 3 )}

- \frac{1}{2} ln (\frac{1}{2}) - \frac{1}{2} ln (\frac{1}{2} + 2)

ln (\frac{1}{1} - 0.1) + 9 ln (\frac{269}{9})

What is 2ln(2)+5ln(x)-1/2 ln(x+3) ?
The solution to 2ln(2)+5ln(x)-1/2 ln(x+3) is ln((4x^5sqrt(x+3))/(x+3))