Giải thích các bước giải:
\(\begin{array}{l}
9,\\
a,\\
230 + \left[ {{2^4} + \left( {x - 5} \right)} \right] = {315.2018^0}\\
\Leftrightarrow 230 + \left[ {16 + x - 5} \right] = 315.1\\
\Leftrightarrow 230 + \left[ {\left( {16 - 5} \right) + x} \right] = 315\\
\Leftrightarrow 230 + \left( {11 + x} \right) = 315\\
\Leftrightarrow \left( {230 + 11} \right) + x = 315\\
\Leftrightarrow 241 + x = 315\\
\Leftrightarrow x = 315 - 241\\
\Leftrightarrow x = 74\\
b,\\
707:\left[ {\left( {{2^x} - 5} \right) + 74} \right] = {4^2} - {3^2}\\
\Leftrightarrow 707:\left[ {{2^x} + \left( {74 - 5} \right)} \right] = 16 - 9\\
\Leftrightarrow 707:\left( {{2^x} + 69} \right) = 7\\
\Leftrightarrow {2^x} + 69 = 707:7\\
\Leftrightarrow {2^x} + 69 = 101\\
\Leftrightarrow {2^x} = 101 - 69\\
\Leftrightarrow {2^x} = 32\\
\Leftrightarrow {2^x} = {2^5}\\
\Leftrightarrow x = 5\\
c,\\
\left[ {\left( {6x - 12} \right):3} \right].32 = 64\\
\Leftrightarrow \left( {6x - 12} \right):3 = 64:32\\
\Leftrightarrow \left[ {6.\left( {x - 2} \right)} \right]:3 = 2\\
\Leftrightarrow 6.\left( {x - 2} \right) = 2.3\\
\Leftrightarrow 6.\left( {x - 2} \right) = 6\\
\Leftrightarrow x - 2 = 6:6\\
\Leftrightarrow x - 2 = 1\\
\Leftrightarrow x = 1 + 2\\
\Leftrightarrow x = 3\\
d,\\
\left( {x:7 + 15} \right).23 = 391\\
\Leftrightarrow x:7 + 15 = 391:23\\
\Leftrightarrow x:7 + 15 = 17\\
\Leftrightarrow x:7 = 17 - 15\\
\Leftrightarrow x:7 = 2\\
\Leftrightarrow x = 2.7\\
\Leftrightarrow x = 14\\
10,\\
a,\\
27 - 7 = 20\\
20 + 30 = 50\\
b,\\
20 + 5 = 25\\
25.2 = 50\\
c,\\
105:5 = 21\\
21 + {3^2} = 30\\
f,\\
20.6 = 120\\
120 - 10 = 110\\
11,\\
a,\\
{2^3}.5 + {3^4}.2 - 4.\left( {{5^7}:{5^5}} \right)\\
= 8.5 + 81.2 - {4.5^{7 - 5}}\\
= 40 + 162 - {4.5^2}\\
= 202 - 100\\
= 102\\
15:\left( {{3^5}:{3^4}} \right) + {5.2^4} - {7^2} - 4\\
= 15:3 + 5.16 - 49 - 4\\
= 5 + 80 - 49 - 4\\
= 32\\
\Rightarrow {2^3}.5 + {3^4}.2 - 4.\left( {{5^7}:{5^5}} \right) > 15:\left( {{3^5}:{3^4}} \right) + {5.2^4} - {7^2} - 4\\
b,\\
\left( {{3^5}{{.3}^7}} \right):{3^{10}} + {5.2^4}\\
= {3^{5 + 7}}:{3^{10}} + 5.16\\
= {3^{12}}:{3^{10}} + 80\\
= {3^{12 - 10}} + 80\\
= {3^2} + 80\\
= 89\\
{5.2^2}{.2^3} - 4.\left( {{5^8}:{5^6}} \right)\\
= {5.2^{2 + 3}} - {4.5^{8 - 6}}\\
= {5.2^5} - {4.5^2}\\
= 5.32 - 4.25\\
= 160 - 100\\
= 60\\
\Rightarrow \left( {{3^5}{{.3}^7}} \right):{3^{10}} + {5.2^4} > {5.2^2}{.2^3} - 4.\left( {{5^8}:{5^6}} \right)\\
c,\\
2.\left[ {\left( {7 - {3^3}:{3^2}} \right):{2^2} + 99} \right] - 100\\
= 2.\left[ {\left( {7 - 3} \right):4 + 99} \right] - 100\\
= 2.\left[ {4:4 + 99} \right] - 100\\
= 2.\left( {1 + 99} \right) - 100\\
= 2.100 - 100\\
= 200 - 100\\
= 100\\
{3^4}.2 + {2^3}.5 - 7.\left( {{5^2} - 5} \right)\\
= 81.2 + 8.5 - 7.\left( {25 - 5} \right)\\
= 162 + 40 - 7.20\\
= 162 + 40 - 140\\
= 62\\
\Rightarrow 2.\left[ {\left( {7 - {3^3}:{3^2}} \right):{2^2} + 99} \right] - 100 > {3^4}.2 + {2^3}.5 - 7.\left( {{5^2} - 5} \right)\\
d,\\
207:\left\{ {{2^3}.\left[ {\left( {156 - 128} \right):14} \right] + 7} \right\}\\
= 207:\left\{ {8.\left[ {28:14} \right] + 7} \right\}\\
= 207:\left\{ {8.2 + 7} \right\}\\
= 207:23\\
= 9\\
117:\left\{ {\left[ {79 - 3.\left( {{3^3} - 17} \right)} \right]:7 + 2} \right\}\\
= 117:\left\{ {\left[ {79 - 3.\left( {27 - 17} \right)} \right]:7 + 2} \right\}\\
= 117:\left\{ {\left[ {79 - 3.10} \right]:7 + 2} \right\}\\
= 117:\left\{ {\left( {79 - 30} \right):7 + 2} \right\}\\
= 117:\left\{ {49:7 + 2} \right\}\\
= 117:\left( {7 + 2} \right)\\
= 117:9\\
= 13\\
207:\left\{ {{2^3}.\left[ {\left( {156 - 128} \right):14} \right] + 7} \right\} < 117:\left\{ {\left[ {79 - 3.\left( {{3^3} - 17} \right)} \right]:7 + 2} \right\}\\
12,\\
a,\\
3{x^3} + 43 = {10^2} - 33\\
\Leftrightarrow 3{x^3} + 43 = 100 - 33\\
\Leftrightarrow 3{x^3} + 43 = 67\\
\Leftrightarrow 3{x^3} = 67 - 43\\
\Leftrightarrow 3{x^3} = 24\\
\Leftrightarrow {x^3} = 24:3\\
\Leftrightarrow {x^3} = 8\\
\Leftrightarrow {x^3} = {2^3}\\
\Leftrightarrow x = 2\\
b,\\
153 - {2.7^x} = 55\\
\Leftrightarrow {2.7^x} = 153 - 55\\
\Leftrightarrow {2.7^x} = 98\\
\Leftrightarrow {7^x} = 98:2\\
\Leftrightarrow {7^x} = 49\\
\Leftrightarrow {7^x} = {7^2}\\
\Leftrightarrow x = 2
\end{array}\)
\(\begin{array}{l}
c,\\
150 - 5.\left( {x - 9} \right) = 25\\
\Leftrightarrow 5.\left( {x - 9} \right) = 150 - 25\\
\Leftrightarrow 5.\left( {x - 9} \right) = 125\\
\Leftrightarrow x - 9 = 125:5\\
\Leftrightarrow x - 9 = 25\\
\Leftrightarrow x = 25 + 9\\
\Leftrightarrow x = 34\\
d,\\
29 + 2x = {3^9}:{3^5}\\
\Leftrightarrow 29 + 2x = {3^{9 - 5}}\\
\Leftrightarrow 29 + 2x = {3^4}\\
\Leftrightarrow 29 + 2x = 81\\
\Leftrightarrow 2x = 81 - 29\\
\Leftrightarrow 2x = 52\\
\Leftrightarrow x = 52:2\\
\Leftrightarrow x = 26\\
e,\\
{2^x} + {2^{x + 1}} = 48\\
\Leftrightarrow {2^x} + {2^x}{.2^1} = 48\\
\Leftrightarrow {2^x} + {2.2^x} = 48\\
\Leftrightarrow {3.2^x} = 48\\
\Leftrightarrow {2^x} = 48:3\\
\Leftrightarrow {2^x} = 16\\
\Leftrightarrow {2^x} = {2^4}\\
\Leftrightarrow x = 4
\end{array}\)\
Em xem lại câu f nhé.
