Exercise 2 Page 488

We can use the fact that $lo g_{4} 3 \approx 0.7925$ and $lo g_{4} 5 \approx 1.1610$ to approximate the value of the given expression. To do so, we will first recall three useful Properties of Logarithms.

	Properties of Logarithms
Name	Product Property	Quotient Property	Power Property
Condition	$a > 0,$ $b > 0,$ and $x \neq = 1$	$a > 0,$ $b > 0,$ and $x \neq = 1$	$m > 0,$ $b > 0,$ and $b \neq = 1$
Property	$lo g_{x} a b = lo g_{x} a + lo g_{x} b$	$lo g_{x} \frac{a}{b} = lo g_{x} a - lo g_{x} b$	$lo g_{b} m^{p} = p lo g_{b} m$

Let's now find the approximation of

lo g_{4} 15 .

We will start by writing

15

as a product of factors.