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

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

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

simplify

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

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

Solution steps

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

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

Simplify

\frac{a + b}{a ^{2} - b ^{2}} : \frac{1}{a - b}

= ln (\frac{1}{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{1}{a - b}) + ln (c^{2})

Apply log rule:

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

ln (\frac{1}{a - b}) + ln (c^{2}) = ln (c^{2} \frac{1}{a - b})

= ln (c^{2} \frac{1}{a - b})

Simplify

\frac{1}{a - b} c^{2} : \frac{c ^{2}}{a - b}

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

3 lo g_{10} (2) + 4 lo g_{10} (x)

5 lo g_{a} (x) - 7 lo g_{a} (y^{6})

lo g_{4} (\frac{1}{4} x^{2} y)

3 ln (2) + 2 ln (x) - \frac{1}{2} \cdot ln (x + 3)

lo g_{10} (5) - lo g_{10} (3)

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