2to the power x÷2³=16 solve it fast
Answers
Answer:
2
2x+1
=17×2
x
−2
3
To find,
The value of x.
Solution,
The step by step solution is shown below :
\begin{gathered}2^{2x+1}=17\times 2^x-2^3\\\\2^{2x+1}=(16+1)\times 2^x-2^3\end{gathered}
2
2x+1
=17×2
x
−2
3
2
2x+1
=(16+1)×2
x
−2
3
Since, 2^4=162
4
=16
So,
\begin{gathered}2^{2x+1}=(2^4+1)\times 2^x-2^3\\\\2^{2x+1}=2^4\times 2^x+2^x-2^3\\\\2^{2x+1}-2^x=2\times 2^3\times 2^x-2^3\\\\2^{2x+1}-2^x=2^3(x^{x+1}-1)\\\\2^x(x^{x+1}-1)=2^3(x^{x+1}-1)\\\\2^x=2^3\end{gathered}
2
2x+1
=(2
4
+1)×2
x
−2
3
2
2x+1
=2
4
×2
x
+2
x
−2
3
2
2x+1
−2
x
=2×2
3
×2
x
−2
3
2
2x+1
−2
x
=2
3
(x
x+1
−1)
2
x
(x
x+1
−1)=2
3
(x
x+1
−1)
2
x
=2
3
We know that, if base are same the powers will be equal. So,
x = 3
So, the value of x is 3.
Answer:
2^ x÷2³=16
[2³ =8 ]
2^ x=16/8
2^x=2
hope this will help you~~~~