Solve for X : 3(2x + 1) - 2x + 2 + 5 = 0 - Mathematics

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

Sum

3(2^x + 1) - 2^{x + 2} + 5 = 0
⇒ 3 x 2^x + 3 - 2^x x 2² + 5 = 0
⇒ 2^x ( 3 - 4 ) + 8 = 0
⇒ - 2^x= - 8
⇒ 2^x= 2³⇒ x = 3

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Solving Exponential Equations

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Chapter 7: Indices (Exponents) - Exercise 7 (B) [Page 101]

Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 14.5 | Page 101

Solve for x:

`3^(4x + 1) = (27)^(x + 1)`

Solve:

2^2x + 2^x+2 − 4 × 2³ = 0

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

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

If a^x = b^y = c^z and b² = ac, prove that: y = `[2xz]/[x + z]`

Solve for x:

`sqrt((3/5)^(x + 3)) = (27^-1)/(125^-1)`

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`

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

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