Solve for X: 5x2 : 5x = 25 : 1 - Mathematics

Solve for x:
5^x2 : 5^x= 25 : 1

Sum

5^x2 : 5^x= 25 : 1
⇒ `(5x^2)/(5x) = (25)/(1)`

⇒ `(5x^2)/(5x) = (5^2)/(1)`

⇒ 5^x2 = 5² x 5^x
⇒ 5^x2 = 5^2+x
⇒ x²= 2 + x
⇒ x² - x - 2 = 0
⇒ (x - 2)(x + 1) = 0
⇒ x - 2 = 0 or x + 1 = 0
⇒ x = 2 or x = -1.

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Solving Exponential Equations

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 9.12

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`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`

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`(2^6 xx 5^-4 xx 3^-3 xx 4^2)/(8^3 xx 15^-3 xx 25^-1)`

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