Question

How do you solve `119/(e^(6x)-14)=7`?

Answer 1

`x=1/6ln31`

Explanation:

`frac{119}{e^(6x)-14}=7`

Multiply each side by `(e^(6x)-14):`
`119=7(e^(6x)-14)`

Divide each side by 7:
`17=e^(6x)-14`

Add 14 to each side:
`31=e^(6x)`

Take the natural log of each side:
`ln(31)=ln(e^(6x))`

`6x=ln31`

Divide each side by 6:
`x=1/6ln31`

Check answer by confirming `e^(6x)-14 cancel=0` (Make sure denominator of original equation is not zero)
`e^(6x)=14`
`6x=ln14`
`x=1/6ln14`
`1/6ln31cancel=ln14`