Explain the properties and the processes you have to use to solve the following logarithmic equation: log base 3 of x + log base 3 of 4 - 2log base 3 of 3 = 2

x = 20.25

Step-by-step explanation:

Given logarithmic equation is  

⇒ {Since we know the logarithmic property }

⇒

⇒ {Since, we know the logarithmic property that }

⇒ {Converting from logarithm to exponent form}

{Since we know that, if then we can write }

⇒ 4x = 81

⇒ x = 20.25 (Answer)

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet