Question

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

Answer 1

Answer:$ln(x^{\frac{1}{4}}y^{\frac{1}{2}}z^{\frac{2}{3}})$

Step-by-step explanation:

Formula:

$k\times ln(a)=ln(a^{k})$

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

$ln(a)-ln(b)=ln(\frac{a}{b})$

$\frac{1}{4}\times ln(x)=ln(x^{\frac{1}{4}})$

$\frac{-1}{2}\times ln(x)=ln(x^{\frac{-1}{2}})$

$\frac{2}{3}\times ln(x)=ln(x^{\frac{2}{3}})$

Working:

So,$\frac{1}{4}ln(x)-\frac{1}{2}ln(y)+\frac{2}{3}ln(z)=ln(x^\frac{1}{4})-ln(y^\frac{-1}{2})+ln(z^\frac{2}{3})$

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

=$ln(x^\frac{1}{4}}{y^{\frac{1}{2}}z^{\frac{2}{3} })$