Question

Use the properties of logarithms to rewrite each expression in an equivalent form containing a single logarithm.

Answer 1

Answer:

$\frac{1}{2}\log(16) + \log(3) + \log(\frac{1}{4})$ = log(3)

Step-by-step explanation:

Given equation:

$\frac{1}{2}\log(16) + \log(3) + \log(\frac{1}{4})$

now,

we know the properties of log function as:

1) log(A) + log(B) = log(AB)

2) log(A) - log(B) = $\log(\frac{A}{B})$

3) log(Aᵇ) = b × log(A)

therefore,

using property 3 we get

$\log(16)^{\frac{1}{2}} + \log(3) + \log(\frac{1}{4})$

or

$\log(4) + \log(3) + \log(\frac{1}{4})$

now,

using the property 2 we get

⇒ log(4) + log(3) + log(1) - log(4)

or

⇒ log(3) + log(1)

now,

using the property 1, we get

⇒ log(3 × 1)

or

⇒ log(3)