# Bài 93 trang 131 SGK giải tích 12 nâng cao

##### Hướng dẫn giải

a) Ta có: $${32^{{{x + 5} \over {x - 7}}}} = 0,{25.128^{{{x + 17} \over {x - 3}}}} \Leftrightarrow {2^{{{5\left( {x + 5} \right)} \over {x - 7}}}} = {1 \over 4}{.2^{{{7\left( {x + 17} \right)} \over {x - 3}}}}$$
$$\Leftrightarrow {2^{{{5\left( {x + 5} \right)} \over {x - 7}}}} = {2^{{{7\left( {x + 17} \right)} \over {x - 3}}-2}} \Leftrightarrow {{5\left( {x + 5} \right)} \over {x - 7}} = {{7\left( {x + 17} \right)} \over {x - 3}} - 2\,\,\left( 1 \right)$$
Điều kiện: $$x \ne 3;\,x \ne 7.$$

(1) $$\Leftrightarrow 5\left( {x + 5} \right)\left( {x - 3} \right) = 7\left( {x + 17} \right)\left( {x - 7} \right) - 2\left( {x - 7} \right)\left( {x - 3} \right)$$
$$\Leftrightarrow 80x = 800 \Leftrightarrow x = 10$$ (nhận)
Vậy $$S = \left\{ {10} \right\}$$
$$b)\,{5^{x - 1}} = {10^x}{.2^{ - x}}{.5^{x + 1}} \Leftrightarrow {1 \over 5}{.5^x} = {{{{10}^x}} \over {{2^x}}}{.5.5^x} \Leftrightarrow {1 \over 5} = {5^x}.5 \Leftrightarrow {5^x} = {1 \over {25}} \Leftrightarrow x = - 2$$
Vậy $$S = \left\{ { - 2} \right\}$$

\eqalign{ & c)\,\,{4^x} - {3^{x - 0,5}} = {3^{x + 0,5}} - {2^{2x - 1}} \Leftrightarrow {4^x} + {1 \over 2}{.4^x} = {3^{x - 0,5}} + {3^{x + 0,5}} \cr & \,\, \Leftrightarrow {3 \over 2}{.4^x} = {3^{x - 0,5}}\left( {1 + 3} \right) \Leftrightarrow {1 \over 2}{.4^{x - 1}} = {3^{x - 1,5}} \cr & \,\, \Leftrightarrow {4^{x - 1,5}} = {3^{x - 1,5}} \Leftrightarrow {\left( {{4 \over 3}} \right)^{x - 1,5}} = 1 \Leftrightarrow x - 1,5 = 0 \cr & \,\,\, \Leftrightarrow x = 1,5 \cr}

Vậy $$S = \left\{ {1,5} \right\}$$
d) Đặt $$t = {3^{2x + 4}}\,\left( {t > 0} \right)$$
Ta có phương trình: $${t^2} - 12t + 28 = 1 \Leftrightarrow {t^2} - 12t + 27 = 0$$

\eqalign{ & \Leftrightarrow \left[ \matrix{ t = 9 \hfill \cr t = 3 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ {3^{2x + 4}} = 9 \hfill \cr {3^{2x + 4}} = 3 \hfill \cr} \right. \cr & \Leftrightarrow \left[ \matrix{ 2x + 4 = 2 \hfill \cr 2x + 2 = 1 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = - 1 \hfill \cr x = - {3 \over 2} \hfill \cr} \right. \cr}

Vậy $$S = \left\{ { - {3 \over 2}; - 1} \right\}$$