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

The solution to (ln^2(x)-2ln(x))/(x-1) is (ln^2(x))/(x-1)

Popular >

simplify (ln^2(x)-2ln(x))/(x-1)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Cancel the common factor:

x

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

ln^{2} (\frac{1}{x}) = ln^{2} (x)

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

ln (\frac{8}{3.1 4 ^{2}} \cdot \frac{( 230 - 50 )}{( 65 - 50 )})

9.28 + lo g_{10} (\frac{0.15}{0.3})

lo g_{6} (x^{6}) - lo g_{6} (2 x^{2}) - lo g_{6} (x^{3})

ln (\frac{x ^{8} x ^{2} + 6}{( x + 6 ) ^{3}})

ln (\frac{27}{4}) - 1

What is (ln^2(x)-2ln(x))/(x-1) ?
The solution to (ln^2(x)-2ln(x))/(x-1) is (ln^2(x))/(x-1)