Using properties of logarithms in exercise, use the properties of logarithms and a fact that in 2≈ 0.6931 and in 3 ≈1.0986 to approximate the logarithm. then use a calculator to confirm your approximation.
(a) in 6
(b) in 3/2
(c) in 81
(d) in (3)1/2

1) 1.7917

2) 0.4055

3) 4.3944

4) 0.5493

Step-by-step explanation:

We are given the following:

We have to evaluate the following:

1) In 6

Logarithmic property:

2)

Logarithmic property:

3) In 81

Logarithmic property:

4)

Logarithmic property:

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.