What is the answer to (4^x+1)/((4^x))= 161/16 ?

The answer to (4^x+1)/((4^x))= 161/16 is x=(ln(16/145))/(2ln(2))

Solve for x: (4^x+1)/((4^x))= 161/16

The solution is x=(ln(16/145))/(2ln(2))

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

x = \frac{ln ( \frac{16}{145} )}{2 ln ( 2 )}

Decimal Notation

x = - 1.58995 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

4^{x} = u

(u + 1) (u)^{- 1} = \frac{161}{16}

Solve

(u + 1) u^{- 1} = \frac{161}{16} : u = \frac{16}{145}

u = \frac{16}{145}

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = \frac{16}{145} : x = \frac{ln ( \frac{16}{145} )}{2 ln ( 2 )}

x = \frac{ln ( \frac{16}{145} )}{2 ln ( 2 )}

Verify Solutions:

x = \frac{ln ( \frac{16}{145} )}{2 ln ( 2 )}

True

The solution is

x = \frac{ln ( \frac{16}{145} )}{2 ln ( 2 )}

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

2^{x} = - 3

x^{x} = 65536

x, y^{\cdot} + 9 y = e^{2 x} 7

2^{x - 4} = 4^{x - 6}

What is the answer to (4^x+1)/((4^x))= 161/16 ?
The answer to (4^x+1)/((4^x))= 161/16 is x=(ln(16/145))/(2ln(2))
Solve for x: (4^x+1)/((4^x))= 161/16
The solution is x=(ln(16/145))/(2ln(2))