Solve for X: P − 5 = 1 P X + 1

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 : 4^{x - 2} - 2^{x + 1} = 0

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

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

Evaluate the following:

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

Evaluate the following:

`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`

Solve for x:
2^{x + 3} + 2^{x + 1} = 320

If x = `3^(2/3) + 3^(1/3)`, prove that x³ - 9x - 12 = 0

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

If 2400 = 2^x x 3^y x 5^z, find the numerical value of x, y, z. Find the value of 2^-x x 3^y x 5^z as fraction.

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

9^2a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`