What is 1/4 ln(x)+5[ln(x-2)-3/10 ln(x+2)] ?

The solution to 1/4 ln(x)+5[ln(x-2)-3/10 ln(x+2)] is 1/4 ln(x)+5ln(((x-2)(x+2)^{7/10})/(x+2))

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simplify 1/4 ln(x)+5[ln(x-2)-3/10 ln(x+2)]

simplify

\frac{1}{4} ln (x) + 5 [ln (x - 2) - \frac{3}{10} ln (x + 2)]

\frac{1}{4} ln (x) + 5 ln (\frac{( x - 2 ) ( x + 2 ) ^{\frac{7}{10}}}{x + 2})

Solution steps

\frac{1}{4} ln (x) + 5 [ln (x - 2) - \frac{3}{10} ln (x + 2)]

Apply log rule:

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

\frac{3}{10} ln (x + 2) = ln ((x + 2)^{\frac{3}{10}})

= \frac{1}{4} ln (x) + 5 [ln (x - 2) - ln ((x + 2)^{\frac{3}{10}})]

Apply log rule:

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

ln (x - 2) - ln ((x + 2)^{\frac{3}{10}}) = ln (\frac{x - 2}{( x + 2 ) ^{\frac{3}{10}}})

= \frac{1}{4} ln (x) + 5 [ln (\frac{x - 2}{( x + 2 ) ^{\frac{3}{10}}})]

Simplify

\frac{x - 2}{( x + 2 ) ^{\frac{3}{10}}} : \frac{( x - 2 ) ( x + 2 ) ^{\frac{7}{10}}}{x + 2}

= \frac{1}{4} ln (x) + 5 [ln (\frac{( x - 2 ) ( x + 2 ) ^{\frac{7}{10}}}{x + 2})]

Remove parentheses:

(a) = a

= \frac{1}{4} ln (x) + 5 ln (\frac{( x - 2 ) ( x + 2 ) ^{\frac{7}{10}}}{x + 2})

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What is 1/4 ln(x)+5[ln(x-2)-3/10 ln(x+2)] ?
The solution to 1/4 ln(x)+5[ln(x-2)-3/10 ln(x+2)] is 1/4 ln(x)+5ln(((x-2)(x+2)^{7/10})/(x+2))