Solve for X: P3 X P-2 = Px - Mathematics

Solve for x:
p³ x p^-2 = p^x

बेरीज

p³ x p^-2 = p^x
⇒ `"p"^(3+(-2))` = p^x ......(Using a^m x aⁿ = a^m+n)
⇒ p¹ = p^x
⇒ x = 1.

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Solving Exponential Equations

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पाठ 9: Indices - Exercise 9.1

पाठ 9 Indices
Exercise 9.1 | Q 9.07

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

If 5^{x + 1} = 25^{x - 2}, find the value of 3^{x - 3} × 2^{3 - x}.

If m ≠ n and (m + n)^-1 (m^-1 + n^-1) = m^xn^y, show that : x + y + 2 = 0

If `((a^-1b^2 )/(a^2b^-4))^7 ÷ (( a^3b^-5)/(a^-2b^3))^-5 = a^x . b^y` , find x + y.

If 3^{x + 1} = 9^{x - 3}, find the value of 2^{1 + x}.

Solve for x:
2^{x + 3} + 2^{x + 1} = 320

Solve for x:
2^2x+3 - 9 x 2^x+ 1 = 0

Solve for x:

`sqrt((3/5)^(x + 3)) = (27^-1)/(125^-1)`

Find the value of k in each of the following:

`root(4)root(3)(x^2)` = x^k

If a^x = b^y = c^z and b² = ac, prove that y = `(2xz)/(z + x)`