Tìm x , biết: 13) ( 3/ 4 ) ^x = 2 ^8/ 3 ^4 .
Giải thích
13) \({\left( {\frac{3}{4}} \right)^x} = \frac{{{2^8}}}{{{3^4}}}\).
\({\left( {\frac{3}{4}} \right)^x} = \frac{{{2^{2.4}}}}{{{3^4}}}\)
\[\frac{{{3^x}}}{{{4^x}}} = \frac{{{{\left( {{2^2}} \right)}^4}}}{{{3^4}}}\]
\[\frac{{{3^x}}}{{{4^x}}} = \frac{{{4^4}}}{{{3^4}}}\]
\[{3^x}{.3^4} = {4^x}{.4^4}\]
\[{3^{x + 4}} = {4^{x + 4}}\]
\(x + 4 = 0\)
\(x = - 4\)
Vậy \(x = - 4\).