What is 3ln(x)+1/2 ln(y)+ln(z) ?

The solution to 3ln(x)+1/2 ln(y)+ln(z) is ln(x^3y^{1/2}z)

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simplify 3ln(x)+1/2 ln(y)+ln(z)

simplify

3 ln (x) + \frac{1}{2} ln (y) + ln (z)

ln (x^{3} y^{\frac{1}{2}} z)

Solution steps

3 ln (x) + \frac{1}{2} ln (y) + ln (z)

Apply log rule:

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

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

= ln (x^{3}) + \frac{1}{2} ln (y) + ln (z)

Apply log rule:

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

\frac{1}{2} ln (y) = ln (y^{\frac{1}{2}})

= ln (x^{3}) + ln (y^{\frac{1}{2}}) + ln (z)

Apply log rule:

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

ln (x^{3}) + ln (y^{\frac{1}{2}}) = ln (x^{3} y^{\frac{1}{2}})

= ln (x^{3} y^{\frac{1}{2}}) + ln (z)

Apply log rule:

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

ln (x^{3} y^{\frac{1}{2}}) + ln (z) = ln (x^{3} z y^{\frac{1}{2}})

= ln (x^{3} y^{\frac{1}{2}} z)

ln (\frac{2 - i}{2 + i})

40 \cdot ln (\frac{0.8}{4})

ln (77)

5 lo g_{10} (x) - 4 lo g_{10} (y)

- lo g_{10} (5 (1 0^{- 6}))

What is 3ln(x)+1/2 ln(y)+ln(z) ?
The solution to 3ln(x)+1/2 ln(y)+ln(z) is ln(x^3y^{1/2}z)