What logarithmic equation has the same solution as x-4=2^3
TO solve for x, Let us add 4 on both sides
But, x=12 is not a logarithmic equation and there are no options
So, an equation like, x=㏒
As log has base 10,
So, x=㏒ =12
So, logarithmic equation like x=log has same solution as x-4=2³
is required lograthmic equation.
Given: Given equation, x - 4 = 2³
To find: Logarithmic function whose solution is same as given equation.
First we find the solution of given Equation.
x - 4 = 2³
x - 4 = 8 ( ∵ 2³ = 2×2×2 = 8 )
x = 8 + 4 ( Transposing 4 to RHS )
x = 12
Now we find the logarithmic equation whose solution is also x = 12.
( There exist many such equations )
Lets say one of them is,
Now we find its solution to check if it is same or not.
(using lograthmic rule,)
⇒ 2 × ( x + 2 ) = 28 (using lograthmic rule, )
⇒ 2x + 4 = 28
⇒ 2x = 28 - 4 (transposing 4 to RHS)
⇒ 2x = 24 (transposing 2 to RHS)
⇒ x = 12
Therefore, is required lograthmic equation.
The solution for the given system of equations are (6, 20).
A system of linear equations is a set of two or more equations involving two or more variables. All of the equations must be considered at once in order to find the solution, which is any pair of values that makes each equation true independently.
The given system of linear equations are y=x+14 -----(i) and y=3x+2 -----(ii).
From equation (i) and (ii), we get
Substitute x=6 equation (i), we get
Therefore, the solution for the given system of equations are (6, 20).
To learn more about the linear system of an equations visit:
(6, 20), because both lines pass through this point
We see that both equations are equal to y. This means we can set the two equations equal to each other:
x+14 = 3x+2
Subtract x from each side:
x+14-x = 3x+2-x
14 = 2x+2
Subtract 2 from each side:
14-2 = 2x+2-2
12 = 2x
Divide both sides by 2:
12/2 = 2x/2
6 = x
Substitute this into the first equation:
y = x+14
y = 6+14
y = 20
This makes the solution (6, 20).
The area of the circular DVD is given by A = 111.33 cm²
A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the area of the circular DVD be A
Let the diameter of the DVD = 12 cm
So , the radius of the DVD = 6 cm
Now , the diameter of the hole = 1.5 cm
So , the radius of the hole = 0.75 cm
And , area of the circular DVD be A = π [ ( 6 )² - ( 0.75 )² ]
On simplifying , we get
The area of circular DVD is A = π ( 36 - 0.5625 )
The area of circular DVD is A = π ( 35.4375 )
The area of circular DVD is A = 111.33 cm²
Hence , the area of the circular DVD is 111.33 cm²
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multiply the others by n
If you want to keep the same ratio, you must multiply all of the numbers by n.
A ratio of 1 : 1 will remain 1 : 1 if all the numbers are multiplied by n:
1 : 1 = n : n
Comment on alternate interpretation of the question
There are occasions for multiplying the ratio by n:
x/n = 1/2
To solve this for x, we multiply the ratio (1/2) by n. This multiplies the numerator, but does not change the denominator.
x = n(1/2) = n/2