Rewrite the equation with the same base.
This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Rewrite the equation with the same base.
We know that $125 = 5^3$. Substitute this into the equation.
$$5^{x+2} = (5^3)^{x-1}$$
Step 2: Apply the exponent rule $(a^m)^n = a^{mn}$.
$$5^{x+2} = 5^{3(x-1)}$$
Step 3: Equate the exponents since the bases are the same.
$$x+2 = 3(x-1)$$
Step 4: Distribute the 3 on the right side of the equation.
$$x+2 = 3x - 3$$
Step 5: Gather terms with $x$ on one side and constant terms on the other side.
Subtract $x$ from both sides:
$$2 = 3x - x - 3$$
$$2 = 2x - 3$$
Add 3 to both sides:
$$2 + 3 = 2x$$
$$5 = 2x$$
Step 6: Solve for $x$.
Divide by 2:
$$x = \frac{5}{2}$$
The solution is:
$$\boxed{x = \frac{5}{2}}$$
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