Question 769062
<pre>
log<sub>3</sub>(x+24) - log<sub>3</sub>(x+2) = 2

Use the logarithm rule {{{log(b,u)-log(b,v)=log(b,u/v)}}} on the left side:

log<sub>3</sub>{{{((x+24)/(x+2))}}} = 2

Use the rule to change a log equation into an exponential equation:

                       {{{log(b,u)=v}}}  becomes {{{u=b^v}}}

{{{(x+24)/(x+2)}}} = 3<sup>2</sup>

{{{(x+24)/(x+2)}}} = 9

Multiply through by (x + 2)

x + 24 = 9(x + 2)

x + 24 = 9x + 18

   -8x = -6

     x = {{{(-6)/(-8)}}}

     x = {{{3/4}}}



Edwin</pre>