What is ln(6p)+3ln(2p-5)-ln(9) ?

The solution to ln(6p)+3ln(2p-5)-ln(9) is ln((2p(2p-5)^3)/3)

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simplify ln(6p)+3ln(2p-5)-ln(9)

simplify

ln (6 p) + 3 ln (2 p - 5) - ln (9)

ln (\frac{2 p ( 2 p - 5 ) ^{3}}{3})

Solution steps

ln (6 p) + 3 ln (2 p - 5) - ln (9)

Apply log rule:

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

3 ln (2 p - 5) = ln ((2 p - 5)^{3})

= ln (6 p) + ln ((2 p - 5)^{3}) - ln (9)

Apply log rule:

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

ln (6 p) + ln ((2 p - 5)^{3}) = ln (6 p (2 p - 5)^{3})

= ln (6 p (2 p - 5)^{3}) - ln (9)

Apply log rule:

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

ln (6 p (2 p - 5)^{3}) - ln (9) = ln (\frac{6 p ( 2 p - 5 ) ^{3}}{9})

= ln (\frac{6 p ( 2 p - 5 ) ^{3}}{9})

Cancel the common factor:

3

= ln (\frac{2 p ( 2 p - 5 ) ^{3}}{3})

2 lo g_{6} (x) + 5 lo g_{6} (y)

\frac{1}{2} ln (\frac{7}{3})

- lo g_{10} (2.46 \cdot 1 0^{- 5})

4 ln (x - 5) - ln (x^{2} - 8 x + 15) + 2 ln (x - 3)

25 lo g_{5} (x) + 5 lo g_{5} (y)

What is ln(6p)+3ln(2p-5)-ln(9) ?
The solution to ln(6p)+3ln(2p-5)-ln(9) is ln((2p(2p-5)^3)/3)