Question

anyone help in this please ​

Answer 1

-7

Step-by-step explanation:

(2/5)^(2x+6)×(2/5)^3 = (2/5)^(x+2)

(2/5)^(2x+6+3) = (2/5)^(x+2)

(2/5)^(2x+9) = (2/5)^(x+2)

here both sides' base will get cancel to Each other ;

on equating powers/

2x +9 = x + 2 => x = - 7

Answer 2

Solution :

We have to find the value of x in :

> ( 2/5 )^{2x + 6} × ( 2/5 )^3 = ( 2/5 )^{x+2}

For simplicity lets assume, 2/5 = some a .

> a^( 2x + 6) × a^3 = a^( x + 2)

> a^( 2x + 6 + 3) = a^( x + 2)

> a^( 2x + 9) = a^( x + 2)

When the bases are equal , the exponents are also equal .

> 2x + 9 = x + 2

> x + 9 = 2

> x = -7 .

This is the required answer.

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Additional Information :

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

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