Question

cna u solve thi question step by step i could not understand​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Solution :

We have to solve, for the real values of x -

$4.2^{2x+1} - 9.2^{x} + 1 = 0$

Let us substitute the value of 2^x by a .

>> $4 \multiply 2^{2x} \multiply 2 - 9 \multiply 2^{x} + 1 = 0$

>> $8 \multiply \: [ 2^x ]^2 - 9 \multiply 2^x + 1 = 0$

Substituting :

8a² - 9a + 1 = 0

>> 8a² - 8a - a + 1 = 0

>> 8a( a - 1) - 1(a - 1) = 0

>> (8a - 1)(a - 1) = 0

We get two values of a, 1 and ⅛

For a = 1

2^x = 1 = 2^0

So, x = 0

For a = ⅛

2^x = 1/8 = 2^(-3)

So, x = -3

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