What number, when has "4" as exponent and increases by 4, is equal to the product 26 and 10?
4^4 + 4 = 26 * 10
Ms Sue gave you the answer worked out. If you want to do it algebraically,
let x = the number,
Then (x^4) + 4 = 26*10
Solve for x.
To find the number that satisfies the given conditions, we need to set up an equation. Let's call the unknown number "x."
According to the problem, the number, when raised to the power of 4 (x^4), increases by 4:
(x + 4)^4
We are told that this expression is equal to the product of 26 and 10 (26 * 10):
(x + 4)^4 = 26 * 10
To find the value of x, let's solve this equation:
1. Take the fourth root of both sides to cancel out the exponent of 4:
∛((x + 4)^4) = ∛(26 * 10)
2. Simplify both sides:
x + 4 = ∛(260)
3. Subtract 4 from both sides to isolate x:
x = ∛(260) - 4
Now we need to calculate the exact value of ∛(260). Using a calculator or a mathematical software, we find that ∛(260) is approximately 6.245.
Therefore, the number we are looking for is:
x = 6.245 - 4
x ≈ 2.245
So, the number that satisfies the given conditions, when raised to the power of 4 and increased by 4, is equal to the product of 26 and 10, is approximately 2.245.