What is ln(2a-2l)-ln(2l+2a)+2ln(2a) ?

The solution to ln(2a-2l)-ln(2l+2a)+2ln(2a) is ln((4a^2(a-l))/(l+a))

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simplify ln(2a-2l)-ln(2l+2a)+2ln(2a)

simplify

ln (2 a - 2 l) - ln (2 l + 2 a) + 2 ln (2 a)

ln (\frac{4 a ^{2} ( a - l )}{l + a})

Solution steps

ln (2 a - 2 l) - ln (2 l + 2 a) + 2 ln (2 a)

Apply log rule:

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

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

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

Simplify

\frac{2 a - 2 l}{2 l + 2 a} : \frac{a - l}{l + a}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{a - l}{l + a} (2 a)^{2} : \frac{4 a ^{2} ( a - l )}{l + a}

= ln (\frac{4 a ^{2} ( a - l )}{l + a})

ln (\frac{1}{3} w) + 4 w

- lo g_{10} (5.39 \cdot 1 0^{- 8})

ln (\frac{( x ^{5} )}{2 y ^{6}})

ln (z (z - 8)^{4})

ln (3) ln (\frac{3}{2})

What is ln(2a-2l)-ln(2l+2a)+2ln(2a) ?
The solution to ln(2a-2l)-ln(2l+2a)+2ln(2a) is ln((4a^2(a-l))/(l+a))