What is ln(5)+3ln(x)+4ln(x^2+4) ?

The solution to ln(5)+3ln(x)+4ln(x^2+4) is ln(5x^3(x^2+4)^4)

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simplify ln(5)+3ln(x)+4ln(x^2+4)

simplify

ln (5) + 3 ln (x) + 4 ln (x^{2} + 4)

ln (5 x^{3} (x^{2} + 4)^{4})

Solution steps

ln (5) + 3 ln (x) + 4 ln (x^{2} + 4)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

4 ln (x^{2} + 4) = ln ((x^{2} + 4)^{4})

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

Apply log rule:

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

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

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

ln (\frac{0.75}{0.25})

ln (\frac{3 r ^{2}}{r - 8})

2 ln (2) + 4 ln (x) - \frac{1}{2} ln (x + 9)

lo g_{10} (x^{2})

lo g_{10} (\frac{x}{1000 y ^{4}})

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