Question

3ki power x+3 ki power x+1 = 36, find=x ki power?

Answer 1

$\bold{3 {}^{x} + {3}^{x + 1} = 36 }$


From the laws of exponents. We know that 3^{ m + n } = 3^{ m } × 3^{ n }


Reversing this ↑ process. 3^{ x + 1 } will be 3^{ x } × 3^{ 1 }


$\bold{ {3}^{x} + ( {3}^{x} \times {3}^{1} )= 36} \\ \\ \bold{ {3}^{x} + ( {3}^{x} \times 3) = 36}$



Now, there are two numbers in Left Hand Side [ 3^{ x } and 3^{ x } × 3 ]. On observing both we get that 3^{ x } is common in both the numbers.


$\bold{ {3}^{x}(1 + (1 \times 3)) = 36 } \\ \\ \bold{ {3}^{x} (1 + 3) = 36} \\ \\ \bold{ {3}^{x} (4) = 36}$



Now, dividing both sides by 4,


$\bold{ \dfrac{ {3}^{x} \times 4}{4} = \dfrac{36}{4} } \\ \\ \\ \bold{ {3}^{x} = 9} \\ \\ \bold{ {3}^{x} = {3}^{2} }$



If bases are same, powers are equal. So, in 3^{ x } and 3^{ 2 }, bases i.e. 3 is same. So


$\bold{x = 2}$






Therefore,
Value of the variable x is 2.

Answer 2

3^{ x } + 3^{ x + 1 } = 36

3^{ x } + ( 3^{ x } × 3^{ 1 } ) = 36

3^{ x } ( 1 + 3^{ 1 } ) = 36

3^{ x } ( 1 + 3 ) = 36

3^{ x } ( 4 ) = 36

3^{ x } = 36 / 4

3^{ x } = 9

3^{ x } = 3^{ 2 }


if bases are equal, powers are same,


x = 2

$\:$


Therefore the value of x is 2