Solve for X: P − 5 = 1 P X + 1

Solve for x:

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

योग

`"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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अध्याय 9: Indices - Exercise 9.1

अध्याय 9 Indices
Exercise 9.1 | Q 9.08

Find x, if : 4^2x = `1/32`

If 4^{x + 3} = 112 + 8 × 4^x, find the value of (18x)^3x.

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

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

If 3^{x + 1} = 9^{x - 3}, find the value of 2^{1 + x}.

Evaluate the following:

`(2^6 xx 5^-4 xx 3^-3 xx 4^2)/(8^3 xx 15^-3 xx 25^-1)`

Evaluate the following:

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

Solve for x:
2^2x + 2^{x +2} - 4 x 2³ = 0

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

If 2250 = 2^a. 3^b. 5^c, find a, b and c. Hence, calculate the value of 3^a x 2^-b x 5^-c.