What is the missing exponent in the following equation s/500 s equals s175
To find the missing exponent in the equation s/500 = s^x, we need to solve for x.
Given that s = 175, we can substitute this value into the equation:
175/500 = 175^x
Now we simplify the left-hand side of the equation:
0.35 = 175^x
To solve for x, we need to isolate the variable. We can take the logarithm of both sides of the equation (base 10, for example):
log(0.35) = log(175^x)
Using the logarithmic property, we can bring the exponent down in front:
log(0.35) = x * log(175)
Now we can solve for x by dividing both sides of the equation by log(175):
x = log(0.35) / log(175)
Using a calculator, we can calculate the value of x:
x ≈ -1.589
Therefore, the missing exponent in the equation s/500 = s^x is approximately -1.589.
To find the missing exponent in the equation s/500 = s^x, you need to follow these steps:
1. Start with the given equation: s/500 = s^x.
2. To solve for the missing exponent, you want to isolate the variable "s" on one side of the equation.
3. Multiply both sides of the equation by 500 to eliminate the fraction: s/500 * 500 = s^x * 500.
This simplifies to: s = 500s^x.
4. Now, you want to express both sides of the equation with the same base. Let's express 500 as a power of "s": 500 = s^2 * 5^3.
5. Substitute this expression into the equation: s = (s^2 * 5^3) * s^x.
6. Use the properties of exponents to simplify the equation: s = s^(2 + x) * 5^3.
7. Since the bases on both sides of the equation are the same, the exponents must also be equal: 1 = 2 + x.
8. Solve for the missing exponent "x": 1 - 2 = x.
9. Simplify: x = -1.
Therefore, the missing exponent in the equation s/500 = s^x is x = -1.
The missing exponent in the equation is 2.
The equation can be written as:
s/500 = s^2/175