Solve the following inequality:
$x^{2\log_56}-3\cdot6^{\log_5x}+42\le0$
do you have any ideas on how to run this task?
2026-04-13 04:22:26.1776054146
logarithm inequality solve
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$$x^{2\log_56}-3\cdot6^{\log_5x}+42\le0$$
The trick is that we have $$x^{\log_56}= 6^{\log_5x}$$
thus the equation is changed to $$y^2-3y+42\le 0$$
The above inequality doesn not have any real solution because it is always positive.