To solve for x, we need to isolate it on one side of the equation. In this case, we can do this by taking the eighth root of both sides of the equation.
The eighth root of 120 can be approximated as follows:
- Start by dividing 120 by 2. This gives 60.
- Divide 60 by 2. This gives 30.
- Divide 30 by 2. This gives 15.
- Divide 15 by 2. This gives 7.5.
- Since 2^3 = 8, the eighth root of 120 can be calculated by multiplying 7.5 by 2^(1/8). This gives approximately 2.179.
Therefore, x ≈ 2.179.
Solve for x: x8=120
2 answers
ah, 2.179^8 = 508.227 , not 120
Let's try again.
120^1/8 = 120^0.125 = 1.82 approx
check that
1.8^8 = 120.4 = close enough
brute force
2^8 = 2^4 * 2^4 = 32*32 = 1024
1.5^8 = (1.5^2)^4 = 2.25*2.25 *2.25*2.25 = 25.6
etc
Let's try again.
120^1/8 = 120^0.125 = 1.82 approx
check that
1.8^8 = 120.4 = close enough
brute force
2^8 = 2^4 * 2^4 = 32*32 = 1024
1.5^8 = (1.5^2)^4 = 2.25*2.25 *2.25*2.25 = 25.6
etc