<h3>Base Change Property</h3><h3 />
The Base Change Property is very helpful in scenarios related to simplifying equations where the logarithmic terms have a varying base.
So to solve an equation, which possesses logarithmic functions, all logarithmic terms must have a similar base.
<h3>What is Base Change Property?</h3><h3 />
This refers to the base formula which is used to write a logarithm of a number with a base that is fixed as the ratio of two logarithms both having the same base but different from the base of the initial or original logarithm.
Change of Base Formula is given as:
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The example on direct variation is illustrated below based on the information given.
<h3>How to illustrate the direct variation?</h3>
An example will be:
When x = 2, y = 10. Find the value of y when x is 6.
In this case, this will be calculated thus:
y = kx
10 = 2k
k = 10/2
k = 5
Since y = kx.
y = 5 × 6
y = 30
The value of y is 30.
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The equation of the line in standard form is x + 4y = 8
<h3>How to determine the line equation?</h3>
From the question, the points are given as
(0, 2) and (8, 0)
To start with, we must calculate the slope of the line
This is calculated using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 2) and (8, 0)
Substitute the known parameters in Slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
Slope = (0 - 2)/(8 - 0)
Evaluate
Slope = -1/4
The equation of the line can be calculated using as
y - y₁ = m(x + x₁)
Where
(x₁, y₁) = (0, 2)
and
m = slope = -1/4
Substitute the known values in the above equation
So, we have the following equation
y - 2 = -1/4(x - 0)
This gives
y - 2 = -1/4x
Rewrite as
1/4x + y = 2
Multiply by 4
x + 4y = 8
Hence, the line has an equation of x + 4y = 8
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Define x:
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Let the shorter piece be x.
Shorter piece = x
Longer piece = 6x
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Construct equation:
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x +6x =35
7x = 35
x =5
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Find the length:
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Shorter length = x = 5 feet
Larger length = 6x = 6(5) = 30 feet
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Answer: The shorter piece is 5 feet.
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Answer:
1304.5 balance after 5 months
Step-by-step explanation:
first you subtract 400 from 1722 to find the balance she will have which is 1322. then you must multiply 3.5 x 5= 17.50. now subtract 17.50 from 1322 and you get her balance after 5 months
