What is (ln(a+x)+ln(a-x)-2ln(a))/(x^2) ?

The solution to (ln(a+x)+ln(a-x)-2ln(a))/(x^2) is (ln(\frac{(a+x)(a-x))/(a^2))}{x^2}

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simplify (ln(a+x)+ln(a-x)-2ln(a))/(x^2)

simplify

\frac{ln ( a + x ) + ln ( a - x ) - 2 ln ( a )}{x ^{2}}

\frac{ln ( \frac{( a + x ) ( a - x )}{a ^{2}} )}{x ^{2}}

Solution steps

\frac{ln ( a + x ) + ln ( a - x ) - 2 ln ( a )}{x ^{2}}

Apply log rule:

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

ln (a + x) + ln (a - x) = ln ((x + a) (- x + a))

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

Apply log rule:

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

2 ln (a) = ln (a^{2})

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

Apply log rule:

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

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

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

ln^{2} (\frac{1}{2}) + 2 ln (\frac{1}{2})

ln (\frac{729}{4}) - 6 ln (2)

lo g_{p} (\frac{p - 1}{2 p \cdot ln ( p )})

lo g_{10} (2 x^{3})

lo g_{7} (3 p^{2})

What is (ln(a+x)+ln(a-x)-2ln(a))/(x^2) ?
The solution to (ln(a+x)+ln(a-x)-2ln(a))/(x^2) is (ln(\frac{(a+x)(a-x))/(a^2))}{x^2}