What is ln((x^8sqrt(p^5q))/(e^2)) ?

The solution to ln((x^8sqrt(p^5q))/(e^2)) is 8ln(x)+ln(sqrt(p)sqrt(q)sqrt(p^4))-2

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simplify ln((x^8sqrt(p^5q))/(e^2))

simplify

ln (\frac{x ^{8} p ^{5} q}{e ^{2}})

8 ln (x) + ln (p q p^{4}) - 2

Solution steps

ln (\frac{x ^{8} p ^{5} q}{e ^{2}})

Apply log rule:

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

ln (\frac{x ^{8} p ^{5} q}{e ^{2}}) = ln (x^{8} p^{5} q) - ln (e^{2})

= ln (x^{8} p^{5} q) - ln (e^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (x^{8} p^{5} q) - 2 ln (e)

Apply log rule:

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

ln (x^{8} p^{5} q) = ln (x^{8}) + ln (p^{5} q)

= ln (x^{8}) + ln (p^{5} q) - 2 ln (e)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{8}) = 8 ln (x)

= 8 ln (x) + ln (p^{5} q) - 2 ln (e)

ln (p^{5} q) = ln (p q p^{4})

2 ln (e) = 2

= 8 ln (x) + ln (p q p^{4}) - 2

lo g_{\frac{1}{2}} (\frac{5}{2})

lo g_{10} (x - 1) - lo g_{10} (x - 2) - lo g_{10} (5)

- \frac{1}{8} lo g_{2} (\frac{1}{8}) - \frac{7}{8} lo g_{2} (\frac{7}{8})

2 lo g_{10} (m) + 3 lo g_{10} (n)

lo g_{3} (y) + lo g_{3} (y + 2)

What is ln((x^8sqrt(p^5q))/(e^2)) ?
The solution to ln((x^8sqrt(p^5q))/(e^2)) is 8ln(x)+ln(sqrt(p)sqrt(q)sqrt(p^4))-2