What is the answer to 49^x+49^{-x}=7 ?

The answer to 49^x+49^{-x}=7 is x=(ln((7+3sqrt(5))/2))/(2ln(7)),x=(ln((7-3sqrt(5))/2))/(2ln(7))

Solve for x: 49^x+49^{-x}=7

The solution is x=(ln((7+3sqrt(5))/2))/(2ln(7)),x=(ln((7-3sqrt(5))/2))/(2ln(7))

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4 9^{x} + 4 9^{- x} = 7

x = \frac{ln ( \frac{7 + 3 5}{2} )}{2 ln ( 7 )}, x = \frac{ln ( \frac{7 - 3 5}{2} )}{2 ln ( 7 )}

Decimal Notation

x = 0.49458 \dots, x = - 0.49458 \dots

Solution steps

4 9^{x} + 4 9^{- x} = 7

Apply exponent rules

4 9^{x} + (4 9^{x})^{- 1} = 7

Rewrite the equation with

4 9^{x} = u

u + (u)^{- 1} = 7

Solve

u + u^{- 1} = 7 : u = \frac{7 + 3 5}{2}, u = \frac{7 - 3 5}{2}

u = \frac{7 + 3 5}{2}, u = \frac{7 - 3 5}{2}

Substitute back

u = 4 9^{x},

solve for

x

Solve

4 9^{x} = \frac{7 + 3 5}{2} : x = \frac{ln ( \frac{7 + 3 5}{2} )}{2 ln ( 7 )}

Solve

4 9^{x} = \frac{7 - 3 5}{2} : x = \frac{ln ( \frac{7 - 3 5}{2} )}{2 ln ( 7 )}

x = \frac{ln ( \frac{7 + 3 5}{2} )}{2 ln ( 7 )}, x = \frac{ln ( \frac{7 - 3 5}{2} )}{2 ln ( 7 )}

3^{a} = 1

x^{l o g_{10} (x)} = 1 0^{9}

ln (3^{x} - 10) = ln (- 8)

6000 (1.05)^{t} = 5500 e^{0.0495 t}

500 = 25 e^{2 x}

What is the answer to 49^x+49^{-x}=7 ?
The answer to 49^x+49^{-x}=7 is x=(ln((7+3sqrt(5))/2))/(2ln(7)),x=(ln((7-3sqrt(5))/2))/(2ln(7))
Solve for x: 49^x+49^{-x}=7
The solution is x=(ln((7+3sqrt(5))/2))/(2ln(7)),x=(ln((7-3sqrt(5))/2))/(2ln(7))