What is the answer to 3^x+4/(3^x)=5 ?

The answer to 3^x+4/(3^x)=5 is x=(2ln(2))/(ln(3)),x=0

Solve for x: 3^x+4/(3^x)=5

The solution is x=(2ln(2))/(ln(3)),x=0

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3^{x} + \frac{4}{3 ^{x}} = 5

x = \frac{2 ln ( 2 )}{ln ( 3 )}, x = 0

Decimal Notation

x = 1.26185 \dots, x = 0

Solution steps

3^{x} + \frac{4}{3 ^{x}} = 5

Apply exponent rules

3^{x} + 4 (3^{x})^{- 1} = 5

Rewrite the equation with

3^{x} = u

u + 4 (u)^{- 1} = 5

Solve

u + 4 u^{- 1} = 5 : 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 : x = 0

x = \frac{2 ln ( 2 )}{ln ( 3 )}, x = 0

Verify Solutions:

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

True

, x = 0

True

The solutions are

x = \frac{2 ln ( 2 )}{ln ( 3 )}, x = 0

9^{x} + 3^{x + 1} = 28

9 \cdot 3^{x} = \frac{1}{27}

8^{x + 4} = 3 2^{3 x}

9^{x} + 3^{x + 1} = 10

4^{x} - 2^{x + 4} + 64 = 0

What is the answer to 3^x+4/(3^x)=5 ?
The answer to 3^x+4/(3^x)=5 is x=(2ln(2))/(ln(3)),x=0
Solve for x: 3^x+4/(3^x)=5
The solution is x=(2ln(2))/(ln(3)),x=0