Log3(2x+8) больше или равно log3(x-2)

[latex]log3(2x+8) \geq log3(x-2)[/latex] [latex]\frac{log(2x+8)}{log(3)}\geq\frac{log(x-2)}{log(3)}[/latex] [latex]log(x+4)-log(x-2)\geq-log(2)[/latex] [latex]log(2(x+4))\geqlog(x-2)[/latex] [latex]x>2[/latex]

[latex]log_3(2x+8)\geq log_3(x-2)[/latex] [latex]\begin{cases} 2x+8>0\\x-2>0\\log_3(2x+8)\geq log_3(x-2) \end{cases} [/latex] [latex]\begin{cases} 2x>-8\\x>2\\2x+8\geq x-2 \end{cases}[/latex] [latex]\begin{cases} x>-4\\x>2\\x\geq -10 \end{cases} [/latex] Ответ х>2 ...............................................................................