Giải các phương trình sau:a) \({(0,3)^{x - 3}} = 1\).b) \({5^{3x - 2}} = 25\).c) \({9^{x - 2}} = {243^{x +
Giải các phương trình sau:
a) \({(0,3)^{x - 3}} = 1\).
b) \({5^{3x - 2}} = 25\).
c) \({9^{x - 2}} = {243^{x + 1}}\).
d) \({\log _{\dfrac{1}{2}}}(x + 1) = - 3\).
e) \({\log _5}(3x - 5) = {\log _5}(2x + 1)\).
g) \({\log _{\dfrac{1}{7}}}(x + 9) = {\log _{\dfrac{1}{7}}}(2x - 1)\).
Đưa về cùng cơ số.
a) \({(0,3)^{x - 3}} = 1 \Leftrightarrow {(0,3)^{x - 3}} = {(0,3)^0} \Leftrightarrow x - 3 = 0 \Leftrightarrow x = 3\)
b) \({5^{3x - 2}} = 25 \Leftrightarrow {5^{3x - 2}} = {5^2} \Leftrightarrow 3x - 2 = 2 \Leftrightarrow 3x = 4 \Leftrightarrow x = \dfrac{4}{3}\)
c) \({9^{x - 2}} = {243^{x + 1}} \Leftrightarrow {3^{2(x - 2)}} = {3^{3(x + 1)}} \Leftrightarrow 2x - 4 = 5x + 5 \Leftrightarrow - 3x = 9 \Leftrightarrow x = - 3\)
d) \({\log _{\dfrac{1}{2}}}(x + 1) = - 3\) ĐКXĐ: \(x + 1 > 0 \Rightarrow x > - 1\)
\({\log _{\dfrac{1}{2}}}(x + 1) = - 3 \Leftrightarrow {\log _{\dfrac{1}{2}}}(x + 1) = {\log _{\dfrac{1}{2}}}(8) \Leftrightarrow x + 1 = 8 \Leftrightarrow x = 7.\)
\(e)\)\({\log _5}(3x - 5) = {\log _5}(2x + 1)\) ĐКXĐ: \(x > \dfrac{5}{3}\)
\({\log _5}(3x - 5) = {\log _5}(2x + 1) \Leftrightarrow 3x - 5 = 2x + 1 \Leftrightarrow x = 6\)
g) \({\log _{\dfrac{1}{7}}}(x + 9) = {\log _{\dfrac{1}{7}}}(2x - 1)\) ĐKXĐ: \(x > \dfrac{1}{2}\)
\({\log _{\dfrac{1}{7}}}(x + 9) = {\log _{\dfrac{1}{7}}}(2x - 1) \Leftrightarrow x + 9 = 2x - 1 \Leftrightarrow x = 10\)
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