What is the answer to 3^x+2/(3^{x-1)}=5 ?

The answer to 3^x+2/(3^{x-1)}=5 is x=1,x=(ln(2))/(ln(3))

Solve for x: 3^x+2/(3^{x-1)}=5

The solution is x=1,x=(ln(2))/(ln(3))

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3^{x} + \frac{2}{3 ^{x - 1}} = 5

x = 1, x = \frac{ln ( 2 )}{ln ( 3 )}

Decimal Notation

x = 1, x = 0.63092 \dots

Solution steps

3^{x} + \frac{2}{3 ^{x - 1}} = 5

Apply exponent rules

3^{x} + 2 (3^{x})^{- 1} \cdot 3^{1} = 5

Rewrite the equation with

3^{x} = u

u + 2 (u)^{- 1} \cdot 3^{1} = 5

Solve

u + 2 u^{- 1} \cdot 3^{1} = 5 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

Solve

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

x = 1, x = \frac{ln ( 2 )}{ln ( 3 )}

Verify Solutions:

x = 1

True

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

True

The solutions are

x = 1, x = \frac{ln ( 2 )}{ln ( 3 )}

625 = 2 5^{x - 10}

0.125 = 128 (\frac{1}{2})^{n}

e^{7 x} = 7

3.25 e^{\frac{0.2}{x}} = 30.6

4^{x + 1} + 2^{2 x - 1} = 288

What is the answer to 3^x+2/(3^{x-1)}=5 ?
The answer to 3^x+2/(3^{x-1)}=5 is x=1,x=(ln(2))/(ln(3))
Solve for x: 3^x+2/(3^{x-1)}=5
The solution is x=1,x=(ln(2))/(ln(3))