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

Solve for x:
p³ x p^-2 = p^x

Sum

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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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 9.07

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

Solve for x : 3(2^x + 1) - 2^{x + 2} + 5 = 0

Evaluate the following:

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

Solve for x:

`"p"^-5 = (1)/"p"^(x + 1)`

Find the value of k in each of the following:

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

If a = `2^(1/3) - 2^((-1)/3)`, prove that 2a³ + 6a = 3

If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0

Find the value of (8p)^p if 9^{p + 2} - 9^p = 240.

If `x^(1/3) + y^(1/3) + z^(1/3) = 0`, prove that (x + y + z)³ = 27xyz

Prove the following:

`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1