Question

Solve 9^2x=66 round to the nearest ten-thousandth

Answer 1

ANSWER

$x = 0.95340$

EXPLANATION

The given expression is

${9}^{2x} = 66$

We take logarithm of both sides to base e to get,

$ln( {9}^{2x} ) = ln(66)$

This implies that,

$2x ln(9) = ln(66)$

Or

$2x ln( {3}^{2} )=ln(66)$

This implies that,

$4x ln(3) = ln(66)$

We divide both sides by 4ln(3) to get,

$x = \frac{ln(66) }{4 ln(3) }$
$x = 0.953397$

To the nearest ten-thousandth, we have,

$x = 0.95340$

Answer 2

If you simplify it, you get x= In(66)/4in(3)
So the answer would be 0.953397... or 1 when you round it
Hope it helps