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Popular >

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

Solution

simplify

ln (x + 2) - ln (x^{2} + 2 x)

Solution

- ln (x)

Solution steps

ln (x + 2) - ln (x^{2} + 2 x)

Apply log rule:

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

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

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

Simplify

\frac{x + 2}{x ^{2} + 2 x} : \frac{1}{x}

= ln (\frac{1}{x})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (x)

Popular Examples

simplify (2.5*ln(2)+ln(3))*0.831 simplify

(2.5 \cdot ln (2) + ln (3)) \cdot 0.831

simplify 2000(ln(140000)-ln(87500))-245 simplify

2000 (ln (140000) - ln (87500)) - 245

simplify 6log_{4}(y-5)-5log_{4}(y+4)simplify

6 lo g_{4} (y - 5) - 5 lo g_{4} (y + 4)

simplify 6log_{b}(w)-1/5 log_{b}(z)+5log_{b}(x)simplify

6 lo g_{b} (w) - \frac{1}{5} lo g_{b} (z) + 5 lo g_{b} (x)

simplify-log_{10}(5.33x10^3)simplify

- lo g_{10} (5.33 x 1 0^{3})

Frequently Asked Questions (FAQ)

What is ln(x+2)-ln(x^2+2x) ?
The solution to ln(x+2)-ln(x^2+2x) is -ln(x)