Answer:
x = 5
Step-by-step explanation:
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FACTS TO KNOW BEFORE SOLVING :-
- [tex]a^x \times a^y = a^{x+y}[/tex]
- In an equation , if the bases are same in both L.H.S. & R.H.S. then , the power of the bases on both the sides of equation should be equal. For e.g. : [tex]a^x = a^y[/tex] ⇒ [tex]x = y[/tex] [∵ Bases are equal on both the sides]
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[tex]4 \times 8^{2x+1} = 32^{x+2}[/tex]
Lets express it in terms of 2.
[tex]=> 2^2 \times 2^{3 (2x+1)} = 2^{5(x+2)}[/tex]
[tex]=> 2^2 \times 2^{6x+3} = 2^{5x+10}[/tex]
[tex]=> 2^{2 + 6x+3} = 2^{5x+10}[/tex]
[tex]=> 2^{6x+5} = 2^{5x+10}[/tex]
Here the bases on both the sides are equal. Hence ,
[tex]=> 6x + 5 = 5x + 10[/tex]
[tex]=> 6x - 5x = 10 - 5[/tex]
[tex]=> x = 5[/tex]
