Question

Combine the terms and write the answer as one logorithm. Please show work.

Answer 1

Answer:
`ln(x^{(1)/(4)}y^{(1)/(2)}z^{(2)/(3)})`

Explanation:

Formula:

`k* ln(a)=ln(a^(k))`

`ln(a)+ln(b)=ln(ab)`

`ln(a)-ln(b)=ln((a)/(b))`

`(1)/(4)* ln(x)=ln(x^{(1)/(4)})`

`(-1)/(2)* ln(x)=ln(x^{(-1)/(2)})`

`(2)/(3)* ln(x)=ln(x^{(2)/(3)})`

Working:

So,
`(1)/(4)ln(x)-(1)/(2)ln(y)+(2)/(3)ln(z)=ln(x^(1)/(4))-ln(y^(-1)/(2))+ln(z^(2)/(3))`

=
`ln(\frac{x^(1)/(4)}{y^{(-1)/(2)} } )+ln(z^{(2)/(3)})`

=
`ln(x^(1)/(4)}{y^{(1)/(2)}z^{(2)/(3) })`