Equation Solving: 25^x-1=125^4x
In this article, we will solve the equation 25^x-1=125^4x and find the value of x.
Step 1: Simplify the Equation
First, let's simplify the equation by expressing both sides in terms of the same base, which is 5.
125 = 5^3, so we can rewrite the equation as:
25^x - 1 = (5^3)^4x 25^x - 1 = 5^(12x)
Step 2: Equate the Exponents
Since the bases are the same, we can equate the exponents:
x = 12x
Step 3: Solve for x
Subtracting 12x from both sides gives:
-11x = -1
Dividing both sides by -11 gives:
x = 1/11
Conclusion
Therefore, the value of x is 1/11.
Note: You can verify this solution by plugging x = 1/11 back into the original equation.
