Question

solve for x: 2^2x+1=17.(2)^x-2^3

Answer 1

Given that,

$2^{2x+1}=17\times 2^x-2^3$

To find,

The value of x.

Solution,

The step by step solution is shown below :

$2^{2x+1}=17\times 2^x-2^3\\\\2^{2x+1}=(16+1)\times 2^x-2^3$

Since, $2^4=16$

So,

$2^{2x+1}=(2^4+1)\times 2^x-2^3\\\\2^{2x+1}=2^4\times 2^x+2^x-2^3\\\\2^{2x+1}-2^x=2\times 2^3\times 2^x-2^3\\\\2^{2x+1}-2^x=2^3(x^{x+1}-1)\\\\2^x(x^{x+1}-1)=2^3(x^{x+1}-1)\\\\2^x=2^3$

We know that, if base are same the powers will be equal. So,

x = 3

So, the value of x is 3.

Answer 2

Step-by-step explanation:

Given that,

2^{2x+1}=17\times 2^x-2^32

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.