If 4^2x-1 – 16 ^x-1=384 ,then find x
Answers
Answered by
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.
-) :)
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?
we can common 4^2x-1
hey not that one the next step
yeah...here we can take common 4^2x-1
you can write 4^2x-2 as 4^2x-1 × 4^-1 ?
yes thanks bro
acc..to exponent rule
my pleasure bro
my Jupiter bro
:p
Answered by
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
→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
Similar questions