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A)3.5n.52+4.5n:53=19.9765625
5n(3.52+4:53)=185546875
5n.\(\frac{12}{5}\)=185546875
b) \(11\cdot6^{x-1}+2\cdot6^{x+1}=11\cdot6^{11}+2\cdot6^{13}\)
\(\Leftrightarrow11\cdot6^{x-1}+2\cdot6^{x+1}=11\cdot6^{12-1}+2\cdot6^{12+1}\)
\(\Leftrightarrow x=12\)
a: \(\Leftrightarrow3\cdot5^n\cdot25+4\cdot5^n\cdot\dfrac{1}{125}=19\cdot5^{10}\)
\(\Leftrightarrow5^n\cdot\left(75+\dfrac{4}{125}\right)=19\cdot5^{10}\)
\(\Leftrightarrow5^n\simeq2472903,228\)(vô lý)
b: \(\Leftrightarrow6^x\cdot11\cdot\dfrac{1}{6}+2\cdot6^x\cdot6=11\cdot6^{11}+2\cdot6^{11}\cdot36\)
\(\Leftrightarrow6^x\left(\dfrac{11}{6}+12\right)=6^{11}\cdot83\)
\(\Leftrightarrow6^x=6^{12}\)
hay x=12
Bài 1 :
a, Ta có : \(\left(-123\right)+\left|-13\right|+\left(-7\right)\)
= \(\left(-123\right)+13+\left(-7\right)=\left(-117\right)\)
b, Ta có : \(\left|-10\right|+\left|45\right|+\left(-\left|-455\right|\right)+\left|-750\right|\)
= \(10+45-455+750=350\)
c, Ta có : \(-\left|-33\right|+\left(-15\right)+20-\left|45-40\right|-57\)
= \(\left(-33\right)+\left(-15\right)+20-5-57=-90\)
a: \(\dfrac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5+3^5}\cdot\dfrac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5+2^5+2^5+2^5+2^5}=2^x\)
\(\Leftrightarrow2^x=\dfrac{4^5}{3^5}\cdot\dfrac{6^5}{2^5}=4^5=2^{10}\)
=>x=10
b: \(\left(x-1\right)^{x+4}=\left(x-1\right)^{x+2}\)
\(\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\)
\(\Leftrightarrow x\left(x-1\right)^{x+2}\cdot\left(x-2\right)=0\)
hay \(x\in\left\{0;1;2\right\}\)
c: \(6\left(6-x\right)^{2003}=\left(6-x\right)^{2003}\)
\(\Leftrightarrow5\cdot\left(6-x\right)^{2003}=0\)
\(\Leftrightarrow6-x=0\)
hay x=6
b)11.6x-1+2.6x+1=11.611+2.613
11.6x-1+2.6x+1 = 11. 612-1+ 2. 612+1
=> x= 12
c) 24-x / 165 = 326
24-x / 220= 230
24-x = 250
=> 4-x = 50
x= -46
c) \(\frac{2^{4-x}}{\left(2^4\right)^5}=\left(2^5\right)^6\)
\(2^{4-x}:2^{20}=\left(2^5\right)^6\)
\(2^{4-x}=2^{30}.2^{20}\)
\(2^{4-x}=2^{50}\)
=> \(4-x=50\)
=> \(x=4-50=-46\)
vậy x = -46