What is ln(x)+2/5 ln(5u^2+1) ?

The solution to ln(x)+2/5 ln(5u^2+1) is ln(x(5u^2+1)^{2/5})

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simplify ln(x)+2/5 ln(5u^2+1)

simplify

ln (x) + \frac{2}{5} ln (5 u^{2} + 1)

ln (x (5 u^{2} + 1)^{\frac{2}{5}})

Solution steps

ln (x) + \frac{2}{5} ln (5 u^{2} + 1)

Apply log rule:

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

\frac{2}{5} ln (5 u^{2} + 1) = ln ((5 u^{2} + 1)^{\frac{2}{5}})

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

Apply log rule:

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

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

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

- 9 ln (9 x) - (\frac{1}{9}) ln (2700 - 9 x)

ln (3000) - ln (2000)

lo g_{4} (\frac{1}{42})

lo g_{2} (\frac{8 w}{g ^{3}})

ln (\frac{6.61}{1.74}) \cdot 8.314

What is ln(x)+2/5 ln(5u^2+1) ?
The solution to ln(x)+2/5 ln(5u^2+1) is ln(x(5u^2+1)^{2/5})