Math, asked by Yugandharyo, 1 year ago

If 4^2x-1 – 16 ^x-1=384 ,then find x

Answers

Answered by Paradoxialchampion
66
Heya!!!

4^2x-1 - 16^x-1 = 384

=) 4^2x-1 - (4)^2 (x-1) = 384

=) 4^2x-1 - 4^2x-2 = 384

=) 4^2x-1 ( 1 - 4^-1 ) = 384

=) 4^2x-1 ( 1 - 1/4 ) = 384

=) 4^2x-1 { (4-1) / 4 } = 384

=) 4^2x-1 (3/4) = 384

=) 4^2x-1 = 384 × 4/3

=) 4^2x-1 = 512

=) 4^2x-1 = 2^9

=) (2)^2 (2x-1) = 2^9

=) 2^4x-2 = 2^9

=) 4x-2 = 9

=) 4x = 9+2

=) 4x = 11

=) x = 11/4

Hence, the value of x is 11/4.

Hope it helps u.

-) :)

Paradoxialchampion: you can write 16 as 4^2 n?
Paradoxialchampion: we can common 4^2x-1
Yugandharyo: hey not that one the next step
Paradoxialchampion: yeah...here we can take common 4^2x-1
Paradoxialchampion: you can write 4^2x-2 as 4^2x-1 × 4^-1 ?
Yugandharyo: yes thanks bro
Paradoxialchampion: acc..to exponent rule
Paradoxialchampion: my pleasure bro
Yugandharyo: my Jupiter bro
Paradoxialchampion: :p
Answered by Prashant24IITBHU
26
we have
→4^(2x-1) - 16^(x-1) = 384
→4^(2x-1) - 4^2(x-1) = 384
→4^(2x-1) - 4^(2x-2) = 384
→[4^(2x-1)] ( 1 - 4^(-1) ) = 384
→[4^(2x-1) ]( 1 - (1/4) ) = 384
→[4^(2x-1)] (3/4) = 384
→4^(2x-1) = 384(4/3)
→4^(2x-1) = 512
→4^(2x-1) = 2^9
→2^(2(2x-1)) = 2^9
→2^(4x-2) = 2^9

by comparing powers
→4x-2 = 9
→4x = 9+2
→4x = 11
x = 11/4
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