What is ln(5)+4ln(x)-8ln(y) ?

The solution to ln(5)+4ln(x)-8ln(y) is ln((5x^4)/(y^8))

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simplify ln(5)+4ln(x)-8ln(y)

simplify

ln (5) + 4 ln (x) - 8 ln (y)

ln (\frac{5 x ^{4}}{y ^{8}})

Solution steps

ln (5) + 4 ln (x) - 8 ln (y)

Apply log rule:

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

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

= ln (5) + ln (x^{4}) - 8 ln (y)

Apply log rule:

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

ln (5) + ln (x^{4}) = ln (5 x^{4})

= ln (5 x^{4}) - 8 ln (y)

Apply log rule:

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

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

= ln (5 x^{4}) - ln (y^{8})

Apply log rule:

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

ln (5 x^{4}) - ln (y^{8}) = ln (\frac{5 x ^{4}}{y ^{8}})

= ln (\frac{5 x ^{4}}{y ^{8}})

lo g_{5} (5 x^{- 5})

3 ln (x) + 4 ln (y) - 2 ln (z)

4 ln (x - 5) + \frac{5}{4} ln (x + 1) - 3 ln (x)

lo g_{4} (\frac{64}{x + 7})

3 lo g_{6} (u) + 5 lo g_{6} (v)

What is ln(5)+4ln(x)-8ln(y) ?
The solution to ln(5)+4ln(x)-8ln(y) is ln((5x^4)/(y^8))