ANSWER
[tex]x = 0.95340[/tex]
EXPLANATION
The given expression is
[tex] {9}^{2x} = 66[/tex]
We take logarithm of both sides to base e to get,
[tex] ln( {9}^{2x} ) = ln(66) [/tex]
This implies that,
[tex]2x ln(9) = ln(66) [/tex]
Or
[tex]2x ln( {3}^{2} )=ln(66) [/tex]
This implies that,
[tex]4x ln(3) = ln(66) [/tex]
We divide both sides by 4ln(3) to get,
[tex]x = \frac{ln(66) }{4 ln(3) } [/tex]
[tex]x = 0.953397[/tex]
To the nearest ten-thousandth, we have,
[tex]x = 0.95340[/tex]
