Question

Cineva care poate sa ma ajute la ex 3, va rog? ​

Answer 1

Răspuns:

{7}

Explicație pas cu pas:

C.E. 7x>0 deci x>0 si x≠1, deci x∈(0, 1)∪(1,+∞).

$log_{7}(7x)+log_{x}=3,~=>~log_{7}7+log_{7}x+\dfrac{1}{log_{7}x}=3,~=>~1+ log_{7}x+\dfrac{1}{log_{7}x}=3,~=>~log_{7}x+\dfrac{1}{log_{7}x}=3-1,~=>~log_{7}x+\dfrac{1}{log_{7}x}=2~|*log_{7}x,~=>~(log_{7}x)^{2}+1=2log_{7}x,~=>~(log_{7}x)^{2}-2log_{7}x+1=0,~=>~(log_{7}x-1)^{2}=0,~=>~log_{7}x-1=0,~=>~log_{7}x=1,~=>x=7^{1}=7,~care~convine~C.E.$