What is the answer to (((2)^{3x+2}+(2)^2))/(((2)^{4x+4))}=1 ?

The answer to (((2)^{3x+2}+(2)^2))/(((2)^{4x+4))}=1 is x=-0.36039…

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(((2)^{3x+2}+(2)^2))/(((2)^{4x+4))}=1

\frac{( ( 2 ) ^{3 x + 2} + ( 2 ) ^{2} )}{( ( 2 ) ^{4 x + 4} )} = 1

x = - 0.36039 \dots

Solution steps

\frac{( ( 2 ) ^{3 x + 2} + ( 2 ) ^{2} )}{( ( 2 ) ^{4 x + 4} )} = 1

Apply exponent rules

((2^{x})^{3} \cdot 2^{2} + 2^{2}) (2^{x})^{- 4} \cdot 2^{- 4} = 1

Rewrite the equation with

2^{x} = u

((u)^{3} \cdot 2^{2} + 2^{2}) (u)^{- 4} \cdot 2^{- 4} = 1

Solve

(u^{3} \cdot 2^{2} + 2^{2}) u^{- 4} \cdot 2^{- 4} = 1 : u \approx 0.77894 \dots, u \approx - 0.65199 \dots

u \approx 0.77894 \dots, u \approx - 0.65199 \dots

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 0.77894 \dots : x = - 0.36039 \dots

Solve

2^{x} = - 0.65199 \dots :

No Solution for

x \in R

x = - 0.36039 \dots

Verify Solutions:

x = - 0.36039 \dots

True

The solution is

x = - 0.36039 \dots

k, 2 n \cdot (2^{k} - 2) = 1140

(e) 2^{3 x - 4} = 64

\frac{4 ^{x} + 1}{( 4 ^{x} )} = \frac{161}{16}

e^{x} = \frac{1}{2}

2^{x} = - 3

What is the answer to (((2)^{3x+2}+(2)^2))/(((2)^{4x+4))}=1 ?
The answer to (((2)^{3x+2}+(2)^2))/(((2)^{4x+4))}=1 is x=-0.36039…
Solve for x: (((2)^{3x+2}+(2)^2))/(((2)^{4x+4))}=1
The solution is x=-0.36039…