Question

Write each expression as an equivalent expression with a single logarithm. Assume xx, yy, and zz are positive real

Answer 1

Answer:

$\ln(\frac{xx + yy}{zz})^{\frac{1}{2}}$

Step-by-step explanation:

Given:

1/2(ln(xx + yy) − ln(zz))

Now,

From the properties of log function,

1)  n × ln(x) = ln(xⁿ)

and,

2)  ln(A) - ln(B) = $\ln\frac{A}{B}$

applying the properties in the given equation

we get the above equation as:

$\frac{1}{2}(\ln\frac{xx + yy}{zz})$        

( using the property 2 we get (ln(xx + yy) − ln(zz) = $\ln\frac{xx + yy}{zz}$  

or

⇒ $\ln(\frac{xx + yy}{zz})^{\frac{1}{2}}$    ( using the property 1 i.e n × ln(x) = ln(xⁿ) )

expression as an equivalent expression with a single logarithm is $\ln(\frac{xx + yy}{zz})^{\frac{1}{2}}$