Answer:
can be written as the single logarithm:
Step-by-step explanation:
Start by using in both terms of the expression the property of logarithm of a power that states:
so we recognize that the factor that multiplies each logarithmic expression, can be understood as the power of the argument of the function logarithm:
Then we use the property of logarithm of a product which states that:
So now we recognize the expression:
as the logarithm of the product:
which is finally a single logarithm as requested.
Answer:
a rectangle is twice as long as it is wide . if both its dimensions are increased 4 m , its area is increaed by 88 m squared make a sketch and find its original dimensions of the original rectangle
Step-by-step explanation:
Let l = the original length of the original rectangle
Let w = the original width of the original rectangle
From the description of the problem, we can construct the following two equations
l=2*w (Equation #1)
(l+4)*(w+4)=l*w+88 (Equation #2)
Substitute equation #1 into equation #2
(2w+4)*(w+4)=(2w*w)+88
2w^2+4w+8w+16=2w^2+88
collect like terms on the same side of the equation
2w^2+2w^2 +12w+16-88=0
4w^2+12w-72=0
Since 4 is afactor of each term, divide both sides of the equation by 4
w^2+3w-18=0
The quadratic equation can be factored into (w+6)*(w-3)=0
Therefore w=-6 or w=3
w=-6 can be rejected because the length of a rectangle can't be negative so
w=3 and from equation #1 l=2*w=2*3=6
I hope that this helps. The difficult part of the problem probably was to construct equation #1 and to factor the equation after performing all of the arithmetic operations.
First make each fraction into an improper fraction
2 2/3 = 8/3
1 5/6 = 11/6
Next, make the fractions have same denominators. Note, that what you do to the denominator, you do to the numerator.
8/3(2/2) = 16/6
Add
16/6 + 11/6 = 27/6
27/6 = 4 3/6 = 4 1/2
4 1/2 is your simplified answer
hope this helps
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