Solve the exponential equation. Express irrational solutions in exact form.

Albarellak

Albarellak

Answered question

2021-09-15

Solve the exponential equation. Express irrational solutions in exact form.
614x=5x

Answer & Explanation

un4t5o4v

un4t5o4v

Skilled2021-09-16Added 105 answers

Given exponential equation is
614x=5x
Taking natural log on both sides,
ln(614x)=ln(5x)
We know, ln(ab)=bln(a)
(14x)ln(6)=xln(5)
ln(6)4xln(6)=xln(5)
4xln(6)xln(5)=ln(6)
x[4ln(6)+ln(5)]=ln(6)
x[4ln(6)+ln(5)]=ln(6)
x=ln(6)[4ln(6)+ln(5)]
x0.2042
Answer: The solution set is {ln(6)|4ln(6)+ln(5)|} or {0.2042}

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