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ikadub [295]
4 years ago
9

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

Mathematics
1 answer:
Alekssandra [29.7K]4 years ago
3 0

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}}

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