Question

Đề bài

Giải mỗi phương trình sau:

a)     \({\left( {0,3} \right)^{x - 3}} = 1\)

b)    \({5^{3x - 2}} = 25\)

c)     \({9^{x - 2}} = {243^{x + 1}}\)

d)    \({\log _{\frac{1}{x}}}(x + 1) =  - 3\)

e)     \({\log _5}(3x - 5) = {\log _5}(2x + 1)\)

f)      \({\log _{\frac{1}{7}}}(x + 9) = {\log _{\frac{1}{7}}}(2x - 1)\)

Answer 1

\(a,\left(0,3\right)^{x-3}=1\\ \Leftrightarrow x-3=0\\ \Leftrightarrow x=3\\ b,5^{3x-2}=25\\ \Leftrightarrow3x-2=2\\ \Leftrightarrow3x=4\\ \Leftrightarrow x=\dfrac{4}{3}\\ c,9^{x-2}=243^{x+1}\\ \Leftrightarrow3^{2x-4}=3^{5x+5}\\ \Leftrightarrow2x-4=5x+5\\ \Leftrightarrow3x=-9\\ \Leftrightarrow x=-3\)

Answer 2

d, Điều kiện: \(x>-1;x\ne0\)

\(log_{\dfrac{1}{x}}\left(x+1\right)=-3\\ \Leftrightarrow x+1=x^3\\ x\simeq1,325\left(tm\right)\)

e, Điều kiện: \(x>\dfrac{5}{3}\)

\(log_5\left(3x-5\right)=log_5\left(2x+1\right)\\ \Leftrightarrow3x-5=2x+1\\ \Leftrightarrow x=6\left(tm\right)\)

f, Điều kiện: \(x>\dfrac{1}{2}\)

\(log_{\dfrac{1}{7}}\left(x+9\right)=log_{\dfrac{1}{7}}\left(2x-1\right)\\ \Leftrightarrow x+9=2x-1\\ \Leftrightarrow x=10\left(tm\right)\)