Question

find the value of x if, 7^x-3 multiply by 3 ^2x-8 =441​

Answer 1

      $\underline{\bold{Answer:}}$

      $5$

      $\underline{\bold{Step-by-step-explaination:}}$

      $\text{The given function is }7^{x-3}*3^{2x-8} = 441$

      $\text{Let us start by finding the prime factors of }441$

$\implies \boxed{441 = 7*7*3*3}$

$\implies \boxed{441 = 7^{2} * 3^{2} }$

      $\text{Now substituting the value in the function}$

$\implies \boxed{7^{x-3}*3^{2x-8} = 7^{2} * 3^{2}}$

      $\text{Now comparing the values of the exponents}$

$\implies \boxed{x-3 = 2}$

$\implies \boxed{x = 5}$

      $\text{We can check whether our answer is correct by putting it in } 2x-8 = 2$

$\implies \boxed{2x-8 = 2}$

$\implies \boxed{2(5)-8 = 2}$

$\implies \boxed{10-8 = 2}$

$\implies \boxed{2 = 2}$

 $\therefore \text{ The value of }x \text{ in }7^{x-3}*3^{2x-8} = 441 \text{ is }5$