22x+1= 8⇒ 22x+1= 23⇒ 2x + 1 = 3⇒ 2x = 2⇒ x = 1.

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

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

Sum

2^2x+1= 8
⇒ 2^2x+1= 2³
⇒ 2x + 1 = 3
⇒ 2x = 2
⇒ x = 1.

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Solving Exponential Equations

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 9.01

Solve for x : 2^5x-1 = 4 2^{3x + 1}

If 5^{x + 1} = 25^{x - 2}, find the value of 3^{x - 3} × 2^{3 - x}.

Evaluate the following:

`16^(3/4) + 2(1/2)^-1 xx 3^0`

Solve for x:

`sqrt((8^0 + 2/3)` = (0.6)^2-3x

If a = `2^(1/3) - 2^((-1)/3)`, prove that 2a³ + 6a = 3

Show that : `(1)/(1 + "a"^("p"- "q")) + (1)/(1 + "a"^("q"- "p")`

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.

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

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

Prove the following:

`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1