What is log_{p}((p-1)/(2p*ln(p))) ?

The solution to log_{p}((p-1)/(2p*ln(p))) is log_{p}(p-1)-log_{p}(2)-1-log_{p}(ln(p))

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simplify log_{p}((p-1)/(2p*ln(p)))

simplify

lo g_{p} (\frac{p - 1}{2 p \cdot ln ( p )})

lo g_{p} (p - 1) - lo g_{p} (2) - 1 - lo g_{p} (ln (p))

Solution steps

lo g_{p} (\frac{p - 1}{2 p ln ( p )})

Apply log rule:

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

lo g_{p} (\frac{p - 1}{2 p ln ( p )}) = lo g_{p} (p - 1) - lo g_{p} (2 p ln (p))

= lo g_{p} (p - 1) - lo g_{p} (2 p ln (p))

Apply log rule:

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

lo g_{p} (2 p ln (p)) = lo g_{p} (2) + lo g_{p} (p) + lo g_{p} (ln (p))

= lo g_{p} (p - 1) - (lo g_{p} (2) + lo g_{p} (p) + lo g_{p} (ln (p)))

Apply log rule:

lo g_{a} (a) = 1

= lo g_{p} (p - 1) - (lo g_{p} (2) + lo g_{p} (ln (p)) + 1)

- (lo g_{p} (2) + 1 + lo g_{p} (ln (p))) : - lo g_{p} (2) - 1 - lo g_{p} (ln (p))

= lo g_{p} (p - 1) - lo g_{p} (2) - 1 - lo g_{p} (ln (p))

lo g_{10} (2 x^{3})

lo g_{7} (3 p^{2})

6 lo g_{10} (m) - 6 lo g_{10} (n)

- 0.1386 \cdot ln (\frac{523}{298}) - 0.19867

8.314 \cdot ln (\frac{15000}{2000})

What is log_{p}((p-1)/(2p*ln(p))) ?
The solution to log_{p}((p-1)/(2p*ln(p))) is log_{p}(p-1)-log_{p}(2)-1-log_{p}(ln(p))