What is ln((x^4)/((3x-4)^2)) ?

The solution to ln((x^4)/((3x-4)^2)) is 4ln(x)-2ln(3x-4)

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simplify ln((x^4)/((3x-4)^2))

simplify

ln (\frac{x ^{4}}{( 3 x - 4 ) ^{2}})

4 ln (x) - 2 ln (3 x - 4)

Solution steps

ln (\frac{x ^{4}}{( 3 x - 4 ) ^{2}})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 4 ln (x) - 2 ln (3 x - 4)

\frac{1}{10} ln (\frac{10}{7})

lo g_{7} (\frac{y}{4})

5 + 3 lo g_{10} (\frac{1}{2})

\frac{2}{5} lo g_{10} (m) - \frac{3}{4} lo g_{10} (n)

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