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Answer:

$3^{x-2}+3^x=7290$

$\frac{3^x}{3^2}+3^x=7290$

$3^x(\frac19+1)=7290$

$3^x(\frac{10}{9})=7290$

$3^x=\frac{7290\times 9}{10}$

$3^x=729 \times 9$

$3^x=3^6\times 3^2$

$3^x=3^8$

$x=8$

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