What is 4ln(P)-4ln(75-2P) ?

The solution to 4ln(P)-4ln(75-2P) is ln((P^4)/((75-2P)^4))

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simplify 4ln(P)-4ln(75-2P)

simplify

4 ln (P) - 4 ln (75 - 2 P)

ln (\frac{P ^{4}}{( 75 - 2 P ) ^{4}})

Solution steps

4 ln (P) - 4 ln (75 - 2 P)

Apply log rule:

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

4 ln (P) = ln (P^{4})

= ln (P^{4}) - 4 ln (- 2 P + 75)

Apply log rule:

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

4 ln (- 2 P + 75) = ln ((- 2 P + 75)^{4})

= ln (P^{4}) - ln ((- 2 P + 75)^{4})

Apply log rule:

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

ln (P^{4}) - ln ((75 - 2 P)^{4}) = ln (\frac{P ^{4}}{( - 2 P + 75 ) ^{4}})

= ln (\frac{P ^{4}}{( 75 - 2 P ) ^{4}})

ln (x^{3} y^{7} z)

61.54 ln (\frac{199}{1850})

ln (x - 3 x) + ln (\frac{1}{a})

ln ((0.46 + 5.34 i)^{1.5 e^{1.1}})

ln (\frac{15}{400})

What is 4ln(P)-4ln(75-2P) ?
The solution to 4ln(P)-4ln(75-2P) is ln((P^4)/((75-2P)^4))