How do you solve $ln x = 2(ln 1 - ln 11)$ ?

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Answer 1 · 2016-01-17T04:35:57

$x=1/121$

Divide both sides by $2$ .

$(1/2)lnx=ln1-ln11$

Simplify the right hand side using the logarithm rule: $lna-lnb=ln(a/b)$

$(1/2)lnx=ln(1/11)$

Simplify the left hand side using the logarithm rule: $alnx=ln(x^a)$

$ln(x^(1/2))=ln(1/11)$

$lnsqrtx=ln(1/11)$

Thus, since if $lna=lnb$ , then $a=b$ ,

$sqrtx=1/11$

$x=(1/11)^2$

$x=1/121$

How do you solve ln x = 2(ln 1 - ln 11)ln x = 2(ln 1 - ln 11)?