What is ln(1/((4x-3)^4)) ?

The solution to ln(1/((4x-3)^4)) is -4ln(4x-3)

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simplify ln(1/((4x-3)^4))

simplify

ln (\frac{1}{( 4 x - 3 ) ^{4}})

- 4 ln (4 x - 3)

Solution steps

ln (\frac{1}{( 4 x - 3 ) ^{4}})

Apply log rule:

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

ln (\frac{1}{( 4 x - 3 ) ^{4}}) = ln (1) - ln ((4 x - 3)^{4})

= ln (1) - ln ((4 x - 3)^{4})

Apply log rule:

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

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

= ln (1) - 4 ln (4 x - 3)

Apply log rule:

lo g_{a} (1) = 0

= 0 - 4 ln (4 x - 3)

0 - 4 ln (4 x - 3) = - 4 ln (4 x - 3)

= - 4 ln (4 x - 3)

lo g_{10} (\frac{x ^{8} y ^{9}}{z ^{3}})

lo g_{b} (x) + lo g_{b} (x) + lo g_{b} (3)

ln (\frac{1}{2.6})

lo g_{3} (\frac{x ^{2} ( 2 x + 1 )}{x - 2})

5 lo g_{3} (u) + 6 lo g_{3} (v) + lo g_{3} (w)