Question 1119321
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(NOTE: The use of parentheses WOULD be preferable.  However, using standard rules for interpreting the equation as you show it produces only one meaning.)<br>
{{{ln(x)-3/ln(x)=-2}}}<br>
Multiply both sides by ln(x) to get a "quadratic" in ln(x):<br>
{{{(1n(x))^2-3 = -2ln(x)}}}
{{{(ln(x))^2+2ln(x)-3 = 0}}}
{{{(ln(x)+3)(ln(x)-1) = 0}}}
{{{ln(x) = -3}}}  or  {{{ln(x) = 1}}}
{{{x = e^-3}}}  or  {{{x = e}}}<br>
CHECK...<br>
x = e:  {{{ln(e)-3/ln(e) = 1 - 3/1 = -2}}}  yes<br>
x = e^-3:   {{{ln(e^-3)-3/ln(e^-3) = -3 - (3/-3) = -3+1 = -2}}}  yes