What is ln(((x+5)^4)/(x-2)) ?

The solution to ln(((x+5)^4)/(x-2)) is 4ln(x+5)-ln(x-2)

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simplify ln(((x+5)^4)/(x-2))

simplify

ln (\frac{( x + 5 ) ^{4}}{x - 2})

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

Solution steps

ln (\frac{( x + 5 ) ^{4}}{x - 2})

Apply log rule:

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

ln (\frac{( x + 5 ) ^{4}}{x - 2}) = ln ((x + 5)^{4}) - ln (x - 2)

= ln ((x + 5)^{4}) - ln (x - 2)

Apply log rule:

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

ln ((x + 5)^{4}) = 4 ln (x + 5)

= 4 ln (x + 5) - ln (x - 2)

ln (62)

4 lo g_{6} (y - 3) - 3 lo g_{6} (y + 2)

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

- ln (x) - ln ((\frac{y}{x})^{2} + 1 + \frac{y}{x})

ln ∣ 5 ∣ - 2 ln ∣ 2 ∣

What is ln(((x+5)^4)/(x-2)) ?
The solution to ln(((x+5)^4)/(x-2)) is 4ln(x+5)-ln(x-2)