solving exponential equations: 3^× - 3^-× = 1

[Simboy]

solving exponential equations: 3^× - 3^-× = 1

3^× - 3^-× = 1

{Read as: Three raised to the power x minus three raised to the power negative x equals 1}

 

[Deleted member 4993]

3^× - 3^-× = 1

{Read as: Three raised to the power x minus three raised to the power negative x equals 1}

\(\displaystyle 3^x - 3^{-x} = 1\)

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

substitute

u = 3^x

and continue....

 

[stapel]

3^× - 3^-× = 1

Trick: Multiply through by 3^x:

. . . . .\(\displaystyle 3^{2x}\, -\, 1\, =\, 3^x\)

. . . . .\(\displaystyle 3^{2x}\, -\, 3^x\, -\, 1\, =\, 0\)

. . . . .\(\displaystyle (3^x)^2\, -\, (3^x)\, -\, 1\, =\,0\)

You now have a quadratic in 3^x. Solve (using the Quadratic Formula) for the value(s) for 3^x. Then back-solve for the value(s) of x.