Solve the Expression: 25.2^x - 10^x + 5^x = 25
In this article, we will solve the expression 25.2^x - 10^x + 5^x = 25, where x is a variable.
Step 1: Simplify the Expression
First, let's simplify the expression by noticing that 25 can be written as 5^2. So, we can rewrite the expression as:
5^2.2^x - 10^x + 5^x = 5^2
Step 2: Factor Out Common Terms
Next, let's factor out the common term 5^x from the first two terms:
5^x(2^x.5 - 2^x) + 5^x = 5^2
Step 3: Simplify Further
Now, let's simplify further by combining the two terms with the common factor 5^x:
5^x(2^x.5 - 2^x + 1) = 5^2
Step 4: Solve for x
To solve for x, we can set the expression inside the parentheses equal to 1, since 5^x is never zero:
2^x.5 - 2^x + 1 = 1
Step 5: Simplify and Solve
Now, let's simplify the expression by combining like terms:
2^x(5 - 1) = 0
This implies that:
2^x = 0 or 5 - 1 = 0
Since 2^x can never be zero, we are left with:
5 - 1 = 0
Which implies that x = 1.
Therefore, the solution to the expression 25.2^x - 10^x + 5^x = 25 is x = 1.
Conclusion
In this article, we have successfully solved the expression 25.2^x - 10^x + 5^x = 25, and found that the value of x is 1.
