Solve the following equations.
${6.9}^{0.5 x - 2} + {2.3}^{x - 6} = 56.$

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Solution

$6. 9^{0.5 x - 2} + 2. 3^{x - 6} = (2.3) . 3^{2 (0.5 x - 2)} + 2. 3^{x - 6}$

= $2. 3^{x - 5} + 2. 3^{x - 6} = 56 8. 3^{x - 5} = 56.3$
therefore
$x = 6 + {log}_{3} 7$

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