What is 2[ln(x)+1/4 ln(x+9)] ?

The solution to 2[ln(x)+1/4 ln(x+9)] is 2ln(x(x+9)^{1/4})

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simplify 2[ln(x)+1/4 ln(x+9)]

simplify

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

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

Solution steps

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

Apply log rule:

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

\frac{1}{4} ln (x + 9) = ln ((x + 9)^{\frac{1}{4}})

= 2 [ln (x) + ln ((x + 9)^{\frac{1}{4}})]

Apply log rule:

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

ln (x) + ln ((x + 9)^{\frac{1}{4}}) = ln (x (x + 9)^{\frac{1}{4}})

= 2 [ln (x (x + 9)^{\frac{1}{4}})]

Remove parentheses:

(a) = a

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

lo g_{10} (3) + lo g_{10} (x - 4)

lo g_{10} (x^{\frac{1}{2}} (x + 1)^{3})

lo g_{4} (13 b^{6} c)

lo g_{5} (\frac{25}{x + 2})

lo g_{4} (16 x^{4}) - lo g_{4} ((2 x)^{2})

What is 2[ln(x)+1/4 ln(x+9)] ?
The solution to 2[ln(x)+1/4 ln(x+9)] is 2ln(x(x+9)^{1/4})