Solve for x 25^x=125

Problem

25=125

Solution

1. Identify a common base for both sides of the equation. Both 25 and 125 are powers of 5

2. Rewrite the numbers using the base 5

25=5

125=5

3. Substitute these expressions back into the original equation.

(5)x=5

4. Apply the power rule for exponents, which states (am)n=a(m⋅n)

5(2*x)=5

5. Equate the exponents since the bases are now identical.

2*x=3

6. Solve for x by dividing both sides by 2

x=3/2

Final Answer

25=125⇒x=3/2

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