What is ln((4x^{(2)}-5)(2x-5)^{(3)}) ?

The solution to ln((4x^{(2)}-5)(2x-5)^{(3)}) is ln(4x^2-5)+3ln(2x-5)

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simplify ln((4x^{(2)}-5)(2x-5)^{(3)})

simplify

ln ((4 x^{(2)} - 5) (2 x - 5)^{(3)})

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

Solution steps

ln ((4 x^{(2)} - 5) (2 x - 5)^{(3)})

Apply log rule:

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

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

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

Apply log rule:

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

ln ((2 x - 5)^{(3)}) = 3 ln (2 x - 5)

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

\frac{1}{- 0.03794} ln (\frac{1}{76})

ln (x y) - 3

ln (\frac{16 e ^{- 42}}{( x + 1 ) ^{2}})

\frac{8.31 ( 310 )}{0.000995} ln (\frac{100}{5})

0.423 - \frac{0.0592}{2} lo g_{10} (\frac{0.1}{0.075})

What is ln((4x^{(2)}-5)(2x-5)^{(3)}) ?
The solution to ln((4x^{(2)}-5)(2x-5)^{(3)}) is ln(4x^2-5)+3ln(2x-5)