Solve for X : 22x+1 = 8 - Mathematics

Solve for x : 2^2x+1 = 8

Sum

2^2x+1 = 8
⇒ 2^2x+1 = 2³
We know that if bases are equal, the powers are equal
⇒ 2x + 1 = 3
⇒ 2x = 3 - 1
⇒ 2x = 2
⇒ x = `2/2`
⇒ x = 1

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Solving Exponential Equations

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Chapter 7: Indices (Exponents) - Exercise 7 (B) [Page 100]

Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 1.1 | Page 100

Solve for x:

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

Evaluate : `[(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6`

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:
5^x2 : 5^x= 25 : 1

Find the value of k in each of the following:

`(root(3)(8))^((-1)/(2)` = 2^k

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

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

If `x^(1/3) + y^(1/3) + z^(1/3) = 0`, prove that (x + y + z)³ = 27xyz

Prove the following:

`(x^("a"+"b")/x^"c")^("a"-"b") · (x^("c"+"a")/(x^"b"))^("c"-"a") · ((x^("b"+"c"))/(x"a"))^("b"-"c")` = 1