Question 823317
<pre>
log<sub>4</sub>(2x) - log<sub>4</sub>(x-1) = -1

Use the rule {{{log(B,(A))=log(B,(C))=log(B,(A/C))}}}

log<sub>4</sub>{{{((2x)/(x-1))}}} = -1

Use the rule for changing a logarithm equation to an equivalent
exponential equation: {{{log(B,(A))=C}}} is equivalent to {{{A=B^C}}}:

{{{((2x)/(x-1))}}} = 4<sup>-1</sup>

Use the rule for a negative exponent:

{{{((2x)/(x-1))}}} = {{{1/4}}}

Cross multiply:

8x = x-1
7x = -1
 x = {{{(-1)/7}}}
 x = {{{-1/7}}}

Edwin</pre>