What is 5ln(2)+3ln(x)-1/2 ln(x+9) ?

The solution to 5ln(2)+3ln(x)-1/2 ln(x+9) is ln((32x^3sqrt(x+9))/(x+9))

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simplify 5ln(2)+3ln(x)-1/2 ln(x+9)

simplify

5 ln (2) + 3 ln (x) - \frac{1}{2} ln (x + 9)

ln (\frac{32 x ^{3} x + 9}{x + 9})

Solution steps

5 ln (2) + 3 ln (x) - \frac{1}{2} ln (x + 9)

Apply log rule:

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

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

= ln (2^{5}) + 3 ln (x) - \frac{1}{2} ln (x + 9)

Apply log rule:

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

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

= ln (2^{5}) + ln (x^{3}) - \frac{1}{2} ln (x + 9)

Apply log rule:

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

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

= ln (2^{5} x^{3}) - \frac{1}{2} ln (x + 9)

2^{5} = 32

= ln (32 x^{3}) - \frac{1}{2} ln (x + 9)

Apply log rule:

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

\frac{1}{2} ln (x + 9) = ln ((x + 9)^{\frac{1}{2}})

= ln (32 x^{3}) - ln ((x + 9)^{\frac{1}{2}})

Apply log rule:

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

ln (32 x^{3}) - ln ((x + 9)^{\frac{1}{2}}) = ln (\frac{32 x ^{3}}{( x + 9 ) ^{\frac{1}{2}}})

= ln (\frac{32 x ^{3}}{( x + 9 ) ^{\frac{1}{2}}})

Simplify

\frac{32 x ^{3}}{( x + 9 ) ^{\frac{1}{2}}} : \frac{32 x ^{3} x + 9}{x + 9}

= ln (\frac{32 x ^{3} x + 9}{x + 9})

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ln (\frac{393.62}{390.66})

What is 5ln(2)+3ln(x)-1/2 ln(x+9) ?
The solution to 5ln(2)+3ln(x)-1/2 ln(x+9) is ln((32x^3sqrt(x+9))/(x+9))