Solve 5^(2-x) = 1/125 for x.
5^(2-x) = 1/125
note that we can rewrite 125 as 5^3
thus, we replace the term on the right side of equation:
5^(2-x) = 1/(5^3)
note also that we can still rewrite 1/(5^3) as 5^(-3). thus,
5^(2-x) = 5^(-3)
now that the bases (the 5) are equal, we equate their exponents:
2 - x = -3
-x = -3 - 2
x = 5
hope this helps~ :)
Thankk you! Took me long to figure it out!
To solve the equation 5^(2-x) = 1/125 for x, we need to use logarithms. Here's how you can find the value of x:
Step 1: Rewrite 1/125 as a power of 5. Since 1/125 is equivalent to 5^(-3), we can rewrite the equation as 5^(2-x) = 5^(-3).
Step 2: Since the bases are the same, we can set the exponents equal to each other. This gives us the equation 2-x = -3.
Step 3: Solve for x. To isolate x, first, subtract 2 from both sides of the equation: 2 - x - 2 = -3 - 2. Simplifying, we get -x = -5.
Step 4: Multiply both sides of the equation by -1 to solve for x: -1 * (-x) = -1 * (-5). This gives us x = 5.
Therefore, the value of x that satisfies the equation 5^(2-x) = 1/125 is x = 5.