Question

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

numbers.
1/2(ln(xx + yy) − ln(zz))

Answer 1

`\ln((xx + yy)/(zz))^{(1)/(2)}`

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(A)/(B)`

applying the properties in the given equation

we get the above equation as:

`(1)/(2)(\ln(xx + yy)/(zz))`

( using the property 2 we get (ln(xx + yy) − ln(zz) =
`\ln(xx + yy)/(zz)`

or

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

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