What is ln(x)+2ln(p)-ln(8p^2-1) ?

The solution to ln(x)+2ln(p)-ln(8p^2-1) is ln((xp^2)/(8p^2-1))

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simplify ln(x)+2ln(p)-ln(8p^2-1)

simplify

ln (x) + 2 ln (p) - ln (8 p^{2} - 1)

ln (\frac{x p ^{2}}{8 p ^{2} - 1})

Solution steps

ln (x) + 2 ln (p) - ln (8 p^{2} - 1)

Apply log rule:

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

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

= ln (x) + ln (p^{2}) - ln (8 p^{2} - 1)

Apply log rule:

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

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

= ln (x p^{2}) - ln (8 p^{2} - 1)

Apply log rule:

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

ln (x p^{2}) - ln (8 p^{2} - 1) = ln (\frac{x p ^{2}}{8 p ^{2} - 1})

= ln (\frac{x p ^{2}}{8 p ^{2} - 1})

ln (a + b) + 5 ln (a - b) - 5 ln (c)

ln (\frac{x + 1}{1 - x})

- ln (8) + ln (6) + ln (3) - ln (1)

lo g_{10} (1 0^{x})

- ln (5 \cdot 2) + 1

What is ln(x)+2ln(p)-ln(8p^2-1) ?
The solution to ln(x)+2ln(p)-ln(8p^2-1) is ln((xp^2)/(8p^2-1))