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Question-70196




Question Number 70196 by smartsmith459@gmail.com last updated on 01/Oct/19
Answered by MJS last updated on 01/Oct/19
x=a^(log_b  c) =a^((ln c)/(ln b))   ln x =((ln c)/(ln b))ln a ⇒ x=a^(log_b  c) =c^(log_b  a)   ⇒ 2^(log_3  7) −7^(log_3  2) =0
$${x}={a}^{\mathrm{log}_{{b}} \:{c}} ={a}^{\frac{\mathrm{ln}\:{c}}{\mathrm{ln}\:{b}}} \\ $$$$\mathrm{ln}\:{x}\:=\frac{\mathrm{ln}\:{c}}{\mathrm{ln}\:{b}}\mathrm{ln}\:{a}\:\Rightarrow\:{x}={a}^{\mathrm{log}_{{b}} \:{c}} ={c}^{\mathrm{log}_{{b}} \:{a}} \\ $$$$\Rightarrow\:\mathrm{2}^{\mathrm{log}_{\mathrm{3}} \:\mathrm{7}} −\mathrm{7}^{\mathrm{log}_{\mathrm{3}} \:\mathrm{2}} =\mathrm{0} \\ $$

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