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

The solution to ln(p^4)+ln(3p^5)-2ln(x) is ln((3p^9)/(x^2))

Popular >

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

simplify

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

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

Solution steps

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

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 (x)

Simplify

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 (\frac{14}{3}) - 14 ln (7 (\frac{14}{3}))

ln (k \cdot C^{a})

6 ln (x) + \frac{1}{2} ln (y) - 5

- \frac{9 ln ( \frac{3}{5} )}{2 π l f}

ln (\frac{∣ 5.1 - 2 ∣ ^{2}}{∣ 5.1 - 3 ∣})

What is ln(p^4)+ln(3p^5)-2ln(x) ?
The solution to ln(p^4)+ln(3p^5)-2ln(x) is ln((3p^9)/(x^2))