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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2) + ln (ln (x^{5} - 2 x))

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

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

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

- lo g_{10} (2.8 \cdot 1 0^{- 4})

5 lo g_{10} (x) + 3 lo g_{10} (y)

lo g_{3} (x) + 4 lo g_{3} (y)

\frac{1}{3} ln ∣ y - 1 ∣ - \frac{1}{3} ln ∣ y + 2 ∣

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