Solve for X: P − 5 = 1 P X + 1 - Mathematics

Solve for x:

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

Sum

`"p"^-5 = (1)/"p"^(x + 1)`
⇒ p^-5 x p^{x + 1} = 1
⇒ `"p"^(-5 + x +1)` = 1
⇒ p^x-4= p⁰
⇒ x - 4 = 0
⇒ x = 4.

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Solving Exponential Equations

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 9.08

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

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

Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`

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:

`(12^2 xx 75^-2 xx 35 xx 400)/(48^2 xx 15^-3 xx 525)`

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

Find the value of k in each of the following:

`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3^k

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

If 2^x = 3^y = 12^z ; show that `(1)/z = (1)/y + (2)/x`.

Find the value of 'a' and 'b' if:

`(sqrt243)^"a" ÷ 3^("b" + 1)` = 1 and `27^"b" - 81^(4 -"a"/2)` = 0