Let h(x)=4^(2x-1) find x. h(x)=sqrt(2)

valtricotinevh

valtricotinevh

Answered question

2022-07-27

Let h ( x ) = 4 2 x 1 find x.
h ( x ) = 2

Answer & Explanation

Lance Long

Lance Long

Beginner2022-07-28Added 8 answers

I'm going to assume that you are setting 2 = 4 2 x 1 and then finding x. Let meknow if this is wrong.
2 = 4 2 x 1 take the ln of both sides
ln ( 2 ) = ln 4 2 x 1 use log rules to bring down the exponent
ln ( 2 ) = ( 2 x 1 ) ln ( 4 ) divide both sides by ln ( 4 )
ln ( 2 ) ln ( 4 ) = 2 x 1 the left can be simplified againby using log rules
ln ( 2 ) 2 2 ln ( 2 ) ln ( 2 ) 2 1 2 ln ( 2 ) = 1 4 this is after simplifying theleft side only, now continue
1 4 = 2 x 1 add 1 to both sides
1 4 + 1 = 2 x 1 + 1
5 4 = 2 x divide both sides by 2
5 4 1 2 = 2 x 1 2
5 8 = x (answer)
Freddy Friedman

Freddy Friedman

Beginner2022-07-29Added 5 answers

h ( x ) = 4 2 x 1 ; and given that h ( x ) = 2 ;
so we can say that,
h ( x ) = 4 2 x 1 = 2
4 2 x 1 = 2
( 2 2 ) 2 x 1 = ( 2 ) 1 / 2 .......................[as 4 = 2 2 ]
( 2 ) 2 ( 2 x 1 ) = ( 2 ) 1 / 2 ...................[as (Ax)y =Ax*y]
( 2 ) ( 4 x 2 ) = ( 2 ) 1 / 2
equating the exponent part we can say that,
4x - 2 = 1/2
4 x = 2 + 1 / 2
= 5/2
x = 5 / ( 2 4 )
=5/8
Answer: x = 5/8

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