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 : 9^x+2= 720 + 9^x

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

Find the values of m and n if :
`4^(2m) = ( root(3)(16))^(-6/n) = (sqrt8)^2`

Evaluate : `[(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6`

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

Evaluate the following:

`(8/27)^((-2)/3) - (1/3)^-2 - 7^0`

Solve for x:
1 = p^x

Solve for x:

`sqrt((8^0 + 2/3)` = (0.6)^2-3x

Find the value of k in each of the following:

`(1/3)^-4 ÷ 9^((-1)/(3)` = 3^k

Prove the following:

`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1