Solve (log(7x)) log x = 5

emancipezN

emancipezN

Answered question

2021-05-08

Solve (log(7x))logx=5

Answer & Explanation

Fatema Sutton

Fatema Sutton

Skilled2021-05-09Added 88 answers

We have to solve the following equation
(log(7x))log(x)=5
By applying log rule logc(ab)=logc(a)+logc(b) we get
(log(7x))log(x)=5(log(x)+log(7))log(x)=5   

(u+log(7))u=5,[where u=log(x)]u2+log(7)u5=0

The above is a quadratic equation of the form au2+bu+c=0. By using quadratic formula we get
u=b±b24ac2a=log7±log72+202
Since u=logx, x=eu. Therefore, the required solutions are
x=elog7±(log72)+202

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