Question

)If (7^-3)^2 x 7^x+4 = 7^7, find the value of x.

Answer 1

ANSWER

Step-by-step explanation:

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Answer 2

Answer:

x = 9

Explanation:

As per information provided in the question, We have :

• (7⁻³)² × 7⁽ˣ ⁺ ⁴⁾ = 7⁷

We are asked to find the value of x.

In order to find the value of x, We need to simplify (7⁻³)² × 7⁽ˣ ⁺ ⁴⁾ = 7⁷ using exponential rules.

$\begin{gathered}\longmapsto \rm ( {7}^{ - 3} ) ^{2} \times {7}^{x + 4} = {7}^{7}\end{gathered}$

$\begin{gathered}\longmapsto \rm ( {7}^{ - 3} ) ^{2} \times {7}^{x + 4} = 49\end{gathered}$

$\begin{gathered}\rm Using \: {\big( {a}^{x} \big) }^{y} = {a}^{xy}, \end{gathered}$

$\begin{gathered}\longmapsto \rm {7}^{ - 3 \times 2} \times {7}^{x + 4} = 49\end{gathered}$

$\begin{gathered}\longmapsto \rm {7}^{ - 6} \times {7}^{x + 4} = 49\end{gathered}$

$\begin{gathered}\longmapsto \rm {7}^{ - 6} \times {7}^{x + 4} = {7}^{7}\end{gathered}$

Bases are equal, Thus, We can equate the powers,

$\begin{gathered}\longmapsto \rm { - 6} + {x + 4} = {7}\end{gathered}$

$\begin{gathered}\longmapsto \rm x - 2= {7}\end{gathered}$

$\begin{gathered}\longmapsto \rm x = {7} + 2\end{gathered}$

$\begin{gathered}\longmapsto \rm x = 9\end{gathered}$

∴ The value of x is 9.

Know more :

• An exponent is a constant or variable, It's position is above and to the right side of the given expression.

• An exponent is also known as power.

• Base is the number on which power/exponent is being represented.

$\begin{gathered}\boxed{\begin{array}{cc}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{array}}\end{gathered}$