Solve for X : 22x+1 = 8

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

बेरीज

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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पाठ 7: Indices (Exponents) - Exercise 7 (B) [पृष्ठ १००]

पाठ 7 Indices (Exponents)
Exercise 7 (B) | Q 1.1 | पृष्ठ १००

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

Prove that :
`[ x^(a(b - c))]/[x^b(a - c)] ÷ ((x^b)/(x^a))^c = 1`

Simplify : `[ 3 xx 9^( n + 1 ) - 9 xx 3^(2n)]/[3 xx 3^(2n + 3) - 9^(n + 1 )]`

Solve for x:
2^2x+3 - 9 x 2^x+ 1 = 0

Solve for x:

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

If a^x = b^y = c^z and abc = 1, show that

`(1)/x + (1)/y + (1)/z` = 0.

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

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

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