Question

Find the value of x when 2 to the power x + 4 into 3 2 power x + 1 is equals to 288 is

Answer 1

Given :   2ˣ⁺⁴ . 3ˣ⁺¹   = 288

To find : value of x

Solution:

2ˣ⁺⁴ . 3ˣ⁺¹   = 288

288 = 2 * 144

= 2 * 2 * 72

= 2 * 2 * 2 * 36

= 2 * 2 * 2 * 2 * 18

= 2 * 2  * 2 * 2 * 2 * 9

= 2 * 2  * 2 * 2 * 2 * 3 * 3

= 2⁵ * 3 ²

2ˣ⁺⁴ . 3ˣ⁺¹   =  2⁵ * 3 ²

=> x + 4 = 5     &  x +  1  = 2

=> x = 1        

Value of  x = 1          

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Answer 2

$\mathfrak{Question:}$

$\tt{2^{x+4} \times 3^{x+1}=288}$

$\mathfrak{Solution:}$

$\implies\tt{2^{x+4} \times 3^{x+1}=288}\\\\\\\implies\tt{2^{x+4} \times 3^{x+1}=2^5\times 3^2}\\\\\\\textsf{\underline{After comparing, we get;}}\\\\\\\implies \tt{x+4=5\qquad or, \quad x+1=2}\\\\\\\therefore\quad\tt{x=1.}$