Answer
$x = 4$
Work Step by Step
$4(3^{x}) + 25 = 8(3^{x}) - 299$
$4(3^{x}) - 8(3^{x}) = -299 - 25$
$(4-8)(3^{x}) = -324$
$-4(3^{x}) = -324$
$3^{x} = 81$
$3^{x} = 3^{4}$
$x = 4$
Check:
$4(3^{4}) + 25 \overset{?}{=} 8(3^{4}) - 299$
$4(81) + 25 \overset{?}{=} 8(81) - 299$
$324 + 25 \overset{?}{=} 648 - 299$
$324 + 25 \overset{?}{=} 648 - 299$
$349 = 349$
