Question
Use the like bases property to solve the equation \( 2(5)^{x}=1250 \) \( x= \) Question Help: Video
Ask by Barnett Goodwin. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x=4 \)
Solution
Solve the equation \( 2(5)^{x}=1250 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(2\times 5^{x}=1250\)
- step1: Divide both sides:
\(\frac{2\times 5^{x}}{2}=\frac{1250}{2}\)
- step2: Divide the numbers:
\(5^{x}=625\)
- step3: Rewrite in exponential form:
\(5^{x}=5^{4}\)
- step4: Set the exponents equal:
\(x=4\)
The solution to the equation \(2(5)^{x}=1250\) is \(x=4\).
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Simplify this solution The Deep Dive
To solve the equation \( 2(5)^{x}=1250 \), first, divide both sides by 2 to isolate the exponential term: \( (5)^{x} = \frac{1250}{2} = 625 \). Next, express 625 as a power of 5. Since \( 625 = 5^4 \), you can now set the exponents equal to each other: \( x = 4 \). So, the solution is \( x = 4 \). Another functional way to think about exponents here is that they form a unique identity. Since you have the same base on both sides of the equation (once written as \( 5^4 \)), it’s a clear indicator to match the powers directly. Thus, you simplify the problem significantly and get your answer quickly!
