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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((1 - 2 x)^{3}) = 3 ln (1 - 2 x)

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{lo g _{e} ( a ^{b} ) - lo g _{e} ( a ^{c} )}{b - c}

\frac{lo g _{10} ( 9 x )}{2} - lo g_{10} (\frac{2}{3 x})

ln (\frac{x}{c})

ln (\frac{3}{20})

lo g_{5} (\frac{5 ^{x} x ^{5}}{5 ^{z} z ^{5}})

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