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log-x-x-x-5x-10-x-




Question Number 190802 by mathlove last updated on 12/Apr/23
log_x x=x^(5x−10)      x=?
$${log}_{{x}} {x}={x}^{\mathrm{5}{x}−\mathrm{10}} \:\:\:\:\:{x}=? \\ $$
Answered by gungun last updated on 12/Apr/23
log_a a=1  a^(5a−10) =1  a^(5a−10) =a^0   5a−10=0  a=2  x=2
$$\mathrm{log}_{{a}} {a}=\mathrm{1} \\ $$$${a}^{\mathrm{5}{a}−\mathrm{10}} =\mathrm{1} \\ $$$${a}^{\mathrm{5}{a}−\mathrm{10}} ={a}^{\mathrm{0}} \\ $$$$\mathrm{5}{a}−\mathrm{10}=\mathrm{0} \\ $$$${a}=\mathrm{2} \\ $$$${x}=\mathrm{2} \\ $$
Commented by mathlove last updated on 12/Apr/23
thanks
$${thanks} \\ $$

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