Question

Va rog mult, e urgent!
Ecuatii logaritmice:
log3( 4^x + 2*x^2 - 18) = x*log3(12) - x

Answer 1

$\log_{3}(4^{x}+2*x^{2}-18)=x*\log_{3}{12}-x\\ \\ \log_{3}(4^{x}+2*x^{2}-18)=\log_{3}{12^{x}}-x*\log_{3}3 \\ \\ \log_{3}(4^{x}+2*x^{2}-18)=\log_{3}{12^{x}}-\log_{3}3^{x} \\ \\ \log_{3}(4^{x}+2*x^{2}-18)=\log_{3}(\frac{12^{x}}{3^{x})\\ \\ \log_{3}(4^{x}+2*x^{2}-18)=\log_{3}4^{x}\\ \\ \Rightarrow 4^{x}+2*x^{2}-18=4^{x}\\ \\ 2*x^{2}-18=0\\ \\ 2*x^{2}=18\\ \\ x^{2}=18:2\\ \\ x=\pm \sqrt{9}\\ \\ x=\pm 3\\ \\ S=\{-3;~3\}$