What is the answer to 3^x-4/(3^x)=3 ?

The answer to 3^x-4/(3^x)=3 is x=(2ln(2))/(ln(3))

Solve for x: 3^x-4/(3^x)=3

The solution is x=(2ln(2))/(ln(3))

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3^{x} - \frac{4}{3 ^{x}} = 3

x = \frac{2 ln ( 2 )}{ln ( 3 )}

Decimal Notation

x = 1.26185 \dots

Solution steps

3^{x} - \frac{4}{3 ^{x}} = 3

Apply exponent rules

3^{x} - 4 (3^{x})^{- 1} = 3

Rewrite the equation with

3^{x} = u

u - 4 (u)^{- 1} = 3

Solve

u - 4 u^{- 1} = 3 : u = 4, u = - 1

u = 4, u = - 1

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 4 : x = \frac{2 ln ( 2 )}{ln ( 3 )}

Solve

3^{x} = - 1 :

No Solution for

x \in R

x = \frac{2 ln ( 2 )}{ln ( 3 )}

Verify Solutions:

x = \frac{2 ln ( 2 )}{ln ( 3 )}

True

The solution is

x = \frac{2 ln ( 2 )}{ln ( 3 )}

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

2^{4 x - 3} = 3^{2 - x}

3^{2 x} - 4 \times 3^{x} + 3 = 0

10 \cdot 3^{x + 3} = 60

3^{x} = 64

What is the answer to 3^x-4/(3^x)=3 ?
The answer to 3^x-4/(3^x)=3 is x=(2ln(2))/(ln(3))
Solve for x: 3^x-4/(3^x)=3
The solution is x=(2ln(2))/(ln(3))