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Popular >

simplify ln(((x+2)^6)/(x^5))

Solution

simplify

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

Solution

6 ln (x + 2) - 5 ln (x)

Solution steps

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

Apply log rule:

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

ln (\frac{( x + 2 ) ^{6}}{x ^{5}}) = ln ((x + 2)^{6}) - ln (x^{5})

= ln ((x + 2)^{6}) - ln (x^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 2)^{6}) = 6 ln (x + 2)

= 6 ln (x + 2) - ln (x^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{5}) = 5 ln (x)

= 6 ln (x + 2) - 5 ln (x)

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Frequently Asked Questions (FAQ)

What is ln(((x+2)^6)/(x^5)) ?
The solution to ln(((x+2)^6)/(x^5)) is 6ln(x+2)-5ln(x)