Question

If 4 raised to x+1 = 2 raised to 3x-1 find the value of x​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer :

The value of x is 3

Step-by-step explanation :

Given,

 $\sf 4^{x+1}=2^{3x-1}$

To find,

 the value of x

Solution,

    4 can be written as (2 × 2)

⇒ 4 = 2 × 2

⇒ 4 = 2¹ × 2¹

⇒ 4 = 2¹⁺¹        [ aᵐ + aⁿ = aᵐ⁺ⁿ ]

⇒ 4 = 2²

So,

  $\sf 4^{x+1}=2^{3x-1} \\\\ (2^2)^{x+1}=2^{3x-1} \\\\ 2^{2x+2}=2^{3x-1} \\\\ \textbf{Bases are equal. Exponents must be equal.} \\\\ 2x+2=3x-1 \\\\ 3x-2x=2+1 \\\\ x=3$

The value of x is 3

Verification :

• Put x = 3,

  $\sf 4^{x+1}=2^{3x-1} \\\\ 4^{3+1}=2^{3(3)-1} \\\\ 4^4=2^{9-1} \\\\ 4^4=2^8 \\\\ (2^2)^4=2^8 \\\\ 2^8=2^8 \\\\ LHS=RHS$

Hence verified!

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Laws of exponents :

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Laws of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$