What is ln(a-b)-ln(a+b)+2ln(c) ?

The solution to ln(a-b)-ln(a+b)+2ln(c) is ln((c^2(a-b))/(a+b))

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simplify ln(a-b)-ln(a+b)+2ln(c)

simplify

ln (a - b) - ln (a + b) + 2 ln (c)

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

Solution steps

ln (a - b) - ln (a + b) + 2 ln (c)

Apply log rule:

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

ln (a - b) - ln (a + b) = ln (\frac{a - b}{a + b})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

32 ln (\frac{7}{5}) - 8

4 ln (4) - 6 ln (3) + 2 ln (2) - 2

2 ln (e^{a}) + 3 ln (b^{e})

lo g_{10} (z^{8} y)

3 ln (3) + ln (2^{7})

What is ln(a-b)-ln(a+b)+2ln(c) ?
The solution to ln(a-b)-ln(a+b)+2ln(c) is ln((c^2(a-b))/(a+b))