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Popular >

simplify 3ln(x)-2ln(x+3)

Solution

simplify

3 ln (x) - 2 ln (x + 3)

Solution

ln (\frac{x ^{3}}{( x + 3 ) ^{2}})

Solution steps

3 ln (x) - 2 ln (x + 3)

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln (x^{3}) - 2 ln (x + 3)

Apply log rule:

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

2 ln (x + 3) = ln ((x + 3)^{2})

= ln (x^{3}) - ln ((x + 3)^{2})

Apply log rule:

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

ln (x^{3}) - ln ((x + 3)^{2}) = ln (\frac{x ^{3}}{( x + 3 ) ^{2}})

= ln (\frac{x ^{3}}{( x + 3 ) ^{2}})

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Frequently Asked Questions (FAQ)

What is 3ln(x)-2ln(x+3) ?
The solution to 3ln(x)-2ln(x+3) is ln((x^3)/((x+3)^2))