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

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

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join ln(4)+3ln(x)+4ln(x^2+4)

join

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln ((- 2) e^{- x})

ln (x) - ln (12 - x)

ln ((x - sin (x)) (x + sin (x)))

0.057 - \frac{0.0592}{2} ln (\frac{1}{0.21})

- 0.6 \cdot lo g_{2} (0.6) - (1 - 0.6) \cdot lo g_{2} (1 - 0.6)

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