What is 1/3 ln(x)+4[ln(x-3)-3/8 ln(x+3)] ?

The solution to 1/3 ln(x)+4[ln(x-3)-3/8 ln(x+3)] is 1/3 ln(x)+4ln(((x-3)(x+3)^{5/8})/(x+3))

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simplify 1/3 ln(x)+4[ln(x-3)-3/8 ln(x+3)]

simplify

\frac{1}{3} ln (x) + 4 [ln (x - 3) - \frac{3}{8} ln (x + 3)]

\frac{1}{3} ln (x) + 4 ln (\frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3})

Solution steps

\frac{1}{3} ln (x) + 4 [ln (x - 3) - \frac{3}{8} ln (x + 3)]

Apply log rule:

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

\frac{3}{8} ln (x + 3) = ln ((x + 3)^{\frac{3}{8}})

= \frac{1}{3} ln (x) + 4 [ln (x - 3) - ln ((x + 3)^{\frac{3}{8}})]

Apply log rule:

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

ln (x - 3) - ln ((x + 3)^{\frac{3}{8}}) = ln (\frac{x - 3}{( x + 3 ) ^{\frac{3}{8}}})

= \frac{1}{3} ln (x) + 4 [ln (\frac{x - 3}{( x + 3 ) ^{\frac{3}{8}}})]

Simplify

\frac{x - 3}{( x + 3 ) ^{\frac{3}{8}}} : \frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3}

= \frac{1}{3} ln (x) + 4 [ln (\frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3})]

Remove parentheses:

(a) = a

= \frac{1}{3} ln (x) + 4 ln (\frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3})

5 ln (x) - 2 ln (y)

ln (a + b) + ln (a - b) - 9 ln (c)

lo g_{2} (\frac{x ^{3}}{x - 3})

4 [ln (z) + ln (z + 5)] - 2 ln (z - 5)

ln (x^{2} y)

What is 1/3 ln(x)+4[ln(x-3)-3/8 ln(x+3)] ?
The solution to 1/3 ln(x)+4[ln(x-3)-3/8 ln(x+3)] is 1/3 ln(x)+4ln(((x-3)(x+3)^{5/8})/(x+3))