Hi Sopia:
there are four ways to get the answer for it
1) cube root it
2) Use Logarithms
3) Interpolate it from a graph
4) use the Newton -Rappel method
the simplest way is just cube root it :
Given :
24 =x^3
solve for x
Step 1:
(24)^ 1/3 = (8)^ 1/3 * (4)^ 1/3 taking the factor of 24 ( 8,3 - because 8*3 = 24)
24^ (1/3 ) = 2 *(4^ (1/3)) - solving the cube root of 8 ( because 2^3 = 8) - the exact answer for it ; if you need it
24^(1/3) = 2 * 1.587401051968 - solving the cube root of 4
24(1/3) = 2.884499140615 - Multiplication ( the Approximate answer for it)
Using logarithm
24 = x^3 - given equation from the above
log (24) = log (x^3) - taking the logarithm of both side of the equation to remove the exponent from it
log(24) = 3 log(x) - the power rule of logarithms
log(24) * 1/3 = 1/3* 3log(x) - timing both side of the equation with 1/3 to get the log(x) by itself
log(24) / 3 = log(x) - Multiplication
1.380211241712 / 3 = log(x) - solving the log of 24
0.460070413904 = log (x) - Division of 1.380211241712 by 3
10^0.460070413904 = 10^log(x) - taking the anti-log of both of the equation to remove the logarithm
2.884499140615 = x - solving the anti-logs of both side of the equation
which is the same answer that we got when cube rooting
Proof or check
24= x^3 - given equation
24 = 2.884499140615 * 2.884499140615 *2.884499140615 - Definition of a cube of a number and replacing x with 2.884499140615
24 = 8.320335292208 *2.884499140615 - square of 2.884499140615 or 2.884499140615 multiplied by itself
24 = 24 - Multiplication
It check and equals
So when x = 2.884499140615 and is cubed it make the equation 24 = x^3 true
I hope this helps
there are four ways to get the answer for it
1) cube root it
2) Use Logarithms
3) Interpolate it from a graph
4) use the Newton -Rappel method
the simplest way is just cube root it :
Given :
24 =x^3
solve for x
Step 1:
(24)^ 1/3 = (8)^ 1/3 * (4)^ 1/3 taking the factor of 24 ( 8,3 - because 8*3 = 24)
24^ (1/3 ) = 2 *(4^ (1/3)) - solving the cube root of 8 ( because 2^3 = 8) - the exact answer for it ; if you need it
24^(1/3) = 2 * 1.587401051968 - solving the cube root of 4
24(1/3) = 2.884499140615 - Multiplication ( the Approximate answer for it)
Using logarithm
24 = x^3 - given equation from the above
log (24) = log (x^3) - taking the logarithm of both side of the equation to remove the exponent from it
log(24) = 3 log(x) - the power rule of logarithms
log(24) * 1/3 = 1/3* 3log(x) - timing both side of the equation with 1/3 to get the log(x) by itself
log(24) / 3 = log(x) - Multiplication
1.380211241712 / 3 = log(x) - solving the log of 24
0.460070413904 = log (x) - Division of 1.380211241712 by 3
10^0.460070413904 = 10^log(x) - taking the anti-log of both of the equation to remove the logarithm
2.884499140615 = x - solving the anti-logs of both side of the equation
which is the same answer that we got when cube rooting
Proof or check
24= x^3 - given equation
24 = 2.884499140615 * 2.884499140615 *2.884499140615 - Definition of a cube of a number and replacing x with 2.884499140615
24 = 8.320335292208 *2.884499140615 - square of 2.884499140615 or 2.884499140615 multiplied by itself
24 = 24 - Multiplication
It check and equals
So when x = 2.884499140615 and is cubed it make the equation 24 = x^3 true
I hope this helps
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take the log of both sides.
the rhs (right hand side) will be the log of a multiplication which is the same as the sum of 2 logs (both items).
so you end up with log(24)=log(x)+log(3) I am sure you can solve the rest by solving for x and using 10^whatever.
the rhs (right hand side) will be the log of a multiplication which is the same as the sum of 2 logs (both items).
so you end up with log(24)=log(x)+log(3) I am sure you can solve the rest by solving for x and using 10^whatever.
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24 = x^3
or
x^3 = 24
cube root both sides cbrt = cube root
cbrt(x^3) = cbrt(24)
x = cbrt(24)
simplify
x = cbrt(8*3)
x = cbrt(8) * cbrt(3)
x = 2cbrt(3) <=== x = 2 cubed root of 3
or
x^3 = 24
cube root both sides cbrt = cube root
cbrt(x^3) = cbrt(24)
x = cbrt(24)
simplify
x = cbrt(8*3)
x = cbrt(8) * cbrt(3)
x = 2cbrt(3) <=== x = 2 cubed root of 3
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24=x^3
x=24^(1/3)=2.88449914061
x=24^(1/3)=2.88449914061
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