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C
B
384
解：$\because 27^{x+1}-3^{3x}=234，$
$\therefore 27^{x+1}-(3^3)^x=234，$
$\therefore 27^{x+1}-27^x=234，$
$\therefore 27×27^x - 27^x=234，$
$\therefore 26×27^x=234，$
$\therefore 27^x=9，$
$\therefore (3^3)^x=3^2，$
$\therefore 3^{3x}=3^2，$
$\therefore 3x=2，$
$\therefore x=\frac{2}{3}。$
解：
(1) $\because 4^m=a，$$8^n=b，$
$\therefore 2^{2m}=a，$$2^{3n}=b，$
$\therefore 2^{2m+3n}=2^{2m}·2^{3n}=ab。$
(2) ① $\because 2^{2m}=a，$$2^{3n}=b，$
$\therefore 2^{4m-6n}=2^{4m}÷2^{6n}=(2^{2m})^2÷(2^{3n})^2=\frac{a^2}{b^2}。$
② $\because 2×8^x×16=2^{26}，$
$\therefore 2×(2^3)^x×2^4=2^{26}，$
$\therefore 2×2^{3x}×2^4=2^{26}，$
$\therefore 2^{1+3x+4}=2^{26}，$
$\therefore 1+3x+4=26，$
解得$x=7。$
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