What is ln(((x-3)^2(x+2)^4)/((5x-1)^6)) ?

The solution to ln(((x-3)^2(x+2)^4)/((5x-1)^6)) is 2ln(x-3)+4ln(x+2)-6ln(5x-1)

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simplify ln(((x-3)^2(x+2)^4)/((5x-1)^6))

simplify

ln (\frac{( x - 3 ) ^{2} ( x + 2 ) ^{4}}{( 5 x - 1 ) ^{6}})

2 ln (x - 3) + 4 ln (x + 2) - 6 ln (5 x - 1)

Solution steps

ln (\frac{( x - 3 ) ^{2} ( x + 2 ) ^{4}}{( 5 x - 1 ) ^{6}})

Apply log rule:

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

ln (\frac{( x - 3 ) ^{2} ( x + 2 ) ^{4}}{( 5 x - 1 ) ^{6}}) = ln ((x - 3)^{2} (x + 2)^{4}) - ln ((5 x - 1)^{6})

= ln ((x - 3)^{2} (x + 2)^{4}) - ln ((5 x - 1)^{6})

Apply log rule:

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

ln ((5 x - 1)^{6}) = 6 ln (5 x - 1)

= ln ((x - 3)^{2} (x + 2)^{4}) - 6 ln (5 x - 1)

Apply log rule:

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

ln ((x - 3)^{2} (x + 2)^{4}) = ln ((x - 3)^{2}) + ln ((x + 2)^{4})

= ln ((x - 3)^{2}) + ln ((x + 2)^{4}) - 6 ln (5 x - 1)

Apply log rule:

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

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

= 2 ln (x - 3) + ln ((x + 2)^{4}) - 6 ln (5 x - 1)

Apply log rule:

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

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

= 2 ln (x - 3) + 4 ln (x + 2) - 6 ln (5 x - 1)

2 lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

\frac{1}{3} ln (\frac{14}{7})

ln (5) - 2 ln (2)

- lo g_{10} (7.9 \cdot 1 0^{- 13})

What is ln(((x-3)^2(x+2)^4)/((5x-1)^6)) ?
The solution to ln(((x-3)^2(x+2)^4)/((5x-1)^6)) is 2ln(x-3)+4ln(x+2)-6ln(5x-1)