Solve for X : 22x+1 = 8

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

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

Solve : `(sqrt(3))^( x - 3 ) = ( root(4)(3))^( x + 1 )`

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

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

Solve for x:

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

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

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

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

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

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:

`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1