Solve for X: P3 X P-2 = Px

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 6: Indices - Exercise 9.1

Chapter 6 Indices
Exercise 9.1 | Q 9.07

Solve for x:

`2^(3x + 3) = 2^(3x + 1) + 48`

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

Evaluate the following:

`(2^3 xx 3^5 xx 24^2)/(12^2 xx 18^3 xx 27)`

Solve for x:
3 x 7^x = 7 x 3^x

Solve for x:

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

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

If a^x = b^y = c^z and abc = 1, show that

`(1)/x + (1)/y + (1)/z` = 0.

Prove the following:

`(x^("a"+"b")/x^"c")^("a"-"b") · (x^("c"+"a")/(x^"b"))^("c"-"a") · ((x^("b"+"c"))/(x"a"))^("b"-"c")` = 1

Prove the following:
(x^a)^b-c x (x^b)^c-a x (x^c)^a-b= 1