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Giang ho dai ca viet nham nhé:
\(5.3^x=8.3^9+7.27^3\)
<=> \(5.3^x=8.3^9+7.\left(3^3\right)^3\) <=> \(5.3^x=8.3^9+7.3^9\)
<=> \(5.3^x=15.3^9\) <=> \(3^x=3.3^9=3^{10}\) => x = 10
nhầm chỉnh lại :
\(5.3^x=8.3^9+7.27^3\Rightarrow5.3^x=8.3^9+7.3^9=15.3^9\Rightarrow15.3^{x-1}=15.3^9\Rightarrow3^{x-1}=3^9\Rightarrow x-1=9\Rightarrow x=10\)
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\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left|\left(-\frac{3}{2}\right)+\frac{2}{5}\right|\)
\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\frac{11}{10}\)
\(\left|x-\frac{1}{3}\right|=\frac{3}{10}\)
\(\Rightarrow\hept{\begin{cases}x-\frac{1}{3}=\frac{3}{10}\\x-\frac{1}{3}=-\frac{3}{10}\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{19}{30}\\x=\frac{1}{30}\end{cases}}}\)
Vậy..........
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| x - 4| + | x-5| + | x-6| + | x-7| = 24 - 6x đk 24 - 6x > 0 => x < 4
với x < 4 ta có :
0 > x-4 > x- 5 > x-6 > x - 7
khi đó | x - 4| + | x - 5| + | x-6| + | x - 7| = 24 - 6x
\(\Leftrightarrow\) -( x-4) - (x-5) - (x-6) - ( x-7) = 24 - 6x
-x + 4 - x + 5 - x + 6 - x + 7 = 24 - 6x
- 4x + 22 = 24 - 6x
-4x + 6x = 24 - 22
2x = 2
x = 1(thỏa mãn)
kết luận x = 1 là nghiệm của pt
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\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\left|\left(-3.2\right)+\frac{2}{5}\right|\)
\(\left|x-\frac{1}{3}\right|+\frac{4}{5}=\frac{28}{5}\)
\(\left|x-\frac{1}{3}\right|=\frac{28}{5}-\frac{4}{5}\)
\(\left|x-\frac{1}{3}\right|=\frac{24}{5}\)
\(x=\frac{24}{5}+\frac{1}{3}\)
\(x=\frac{77}{15}\)
\(8.3^x+3.2^x-6^x=24\)
\(\Rightarrow8.3^x+3.2^x-6^x-24=0\)
\(\Rightarrow\left(8.3^x-2^x.3^x\right)-\left(24-3.2^x\right)=0\)
\(\Rightarrow3^x\left(8-2^x\right)-3\left(8-2^x\right)=0\Rightarrow\left(8-2^x\right)\left(3^x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2^x=8\\3^x=3\end{cases}\Rightarrow}\orbr{\begin{cases}x=3\\x=1\end{cases}}\)