Answer

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**Hint:**For answering this question we need to solve the given expression ${{4}^{x+1}}=8$ for getting the value of $x$ . For that we need to use basic arithmetic simplifications like multiplications and transformations like shifting from right hand side to left hand side and reduce it.

**Complete step-by-step solution:**

Now considering from the question we have been asked to solve the given expression ${{4}^{x+1}}=8$.

For doing that we need to use basic arithmetic simplifications like addition, subtraction, multiplication, division and transformations like shifting from right hand side to left hand side and vice-versa then we need to reduce it.

This type of questions is very simple and can be easily answered without performing much calculation and basically we should be sure with this type of questions and try to score maximum out of them.

Here if we observe the given expression is already arranged.

Now we will express $8$ as

$\begin{align}

& \Rightarrow 4\times 2=4\times \sqrt{4}\Rightarrow 4\times {{4}^{\dfrac{1}{2}}} \\

& \Rightarrow {{4}^{1+\dfrac{1}{2}}} \\

\end{align}$

By comparing them we will have $x=\dfrac{1}{2}$ .

**Therefore we can conclude that in the given expression ${{4}^{x+1}}$ the value of $x$ is $\dfrac{1}{2}$.**

**Note:**We should be sure with the simple arithmetic calculations we make to simplify the equations in questions of this type. This type of questions are very easy and do not require much calculations so the possibility of mistakes in questions of this type are very less. Similarly we can simplify any other expressions like for the expression ${{2}^{x}}=16$ it will be given as $\Rightarrow {{2}^{x}}={{2}^{4}}\Rightarrow x=4$ .

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