What is ln((x^3y^4)/(sqrt(z))) ?

The solution to ln((x^3y^4)/(sqrt(z))) is 3ln(x)+4ln(y)-ln(sqrt(z))

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simplify ln((x^3y^4)/(sqrt(z)))

simplify

ln (\frac{x ^{3} y ^{4}}{z})

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

Solution steps

ln (\frac{x ^{3} y ^{4}}{z})

Apply log rule:

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

ln (\frac{x ^{3} y ^{4}}{z}) = ln (x^{3} y^{4}) - ln (z)

= ln (x^{3} y^{4}) - ln (z)

Apply log rule:

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

ln (x^{3} y^{4}) = ln (x^{3}) + ln (y^{4})

= ln (x^{3}) + ln (y^{4}) - ln (z)

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= 3 ln (x) + ln (y^{4}) - ln (z)

Apply log rule:

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

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

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

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ln (\frac{e ^{ρ}}{1 + e ^{ρ}})

10 lo g_{9} (w) + 8 lo g_{9} (x)

ln (20) - ln (10)

ln (\frac{1.39}{1.5})

What is ln((x^3y^4)/(sqrt(z))) ?
The solution to ln((x^3y^4)/(sqrt(z))) is 3ln(x)+4ln(y)-ln(sqrt(z))