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

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 6: Indices - Exercise 9.1

Chapter 6 Indices
Exercise 9.1 | Q 9.12

Solve for x : 2^5x-1 = 4 2^{3x + 1}

Find x, if : `sqrt( 2^( x + 3 )) = 16`

Solve : 8 x 2^2x + 4 x 2^{x + 1} = 1 + 2^x

Solve for x: `4^(x-1) × (0.5)^(3 - 2x) = (1/8)^-x`

Evaluate : `4/(216)^(-2/3) + 1/(256)^(-3/4) + 2/(243)^(-1/5)`

Solve for x:
`9 xx 3^x = (27)^(2x - 5)`

Show that : `(1)/(1 + "a"^("p"- "q")) + (1)/(1 + "a"^("q"- "p")`

If 2250 = 2^a. 3^b. 5^c, find a, b and c. Hence, calculate the value of 3^a x 2^-b x 5^-c.

If 2400 = 2^x x 3^y x 5^z, find the numerical value of x, y, z. Find the value of 2^-x x 3^y x 5^z as fraction.

Prove the following:

`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1