Solve for X: P3 X P-2 = Px

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 : 2^2x+1 = 8

Solve for x : (49)^{x + 4} = 7²x (343)^{x + 1}

Find x, if : `(root(3)( 2/3))^( x - 1 ) = 27/8`

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

If a^x = b, b^y = c and c^z = a, prove that : xyz = 1.

Evaluate the following:

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

Evaluate the following:

`(27)^(2/3) xx 8^((-1)/6) ÷ 18^((-1)/2)`

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

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

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

Prove the following:

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