What is ln(p^4)+ln(3p^5)-2ln(p) ?

The solution to ln(p^4)+ln(3p^5)-2ln(p) is ln(3p^7)

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simplify ln(p^4)+ln(3p^5)-2ln(p)

simplify

ln (p^{4}) + ln (3 p^{5}) - 2 ln (p)

ln (3 p^{7})

Solution steps

ln (p^{4}) + ln (3 p^{5}) - 2 ln (p)

Apply log rule:

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

ln (p^{4}) + ln (3 p^{5}) = ln (3 p^{5} p^{4})

= ln (3 p^{5} p^{4}) - 2 ln (p)

Simplify

p^{4} \cdot 3 p^{5} : 3 p^{9}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{3 p ^{9}}{p ^{2}} : 3 p^{7}

= ln (3 p^{7})

lo g_{3} (92) + \frac{1}{2} lo g_{3} (x)

3 lo g_{3} (u) + 6 lo g_{3} (v) + lo g_{3} (w)

lo g_{10} (2 x^{2} - 5 x - 3) - lo g_{10} (x^{2} - 7 x + 12)

ln (v^{'} (t) - \frac{m ( t ) g ( m ( t ) )}{b}) - ln (- \frac{m ( t ) g ( m ( t ) )}{b})

lo g_{b} (\frac{b b}{( c + 1 ) ^{3}})

What is ln(p^4)+ln(3p^5)-2ln(p) ?
The solution to ln(p^4)+ln(3p^5)-2ln(p) is ln(3p^7)