What is (ln^2(x)+ln(x)-2)(log_{5}(x)-2) ?

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

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simplify (ln^2(x)+ln(x)-2)(log_{5}(x)-2)

simplify

(ln^{2} (x) + ln (x) - 2) (lo g_{5} (x) - 2)

(ln^{2} (x^{2}) - 2) (lo g_{5} (x) - 2)

Solution steps

(ln^{2} (x) + ln (x) - 2) (lo g_{5} (x) - 2)

Apply log rule:

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

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

= (ln^{2} (xx) - 2) (lo g_{5} (x) - 2)

Simplify

xx : x^{2}

= (ln^{2} (x^{2}) - 2) (lo g_{5} (x) - 2)

7 lo g_{5} (x) + 12 lo g_{5} (y)

3 lo g_{10} (x + 5) - lo g_{10} (x - 2)

1.1 \cdot ln (\frac{670}{970}) - \frac{8.314}{28.97} \cdot ln (\frac{1}{4})

ln (2 x^{2} - 2 x - 24) - ln (- 2 x - 6)

- \frac{5}{4} ln (\frac{0.05}{0.9})

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