Move all the terms containing a logarithm to the left side of the equation.<span><span>log<span>(2x+1)</span>−log<span>(x−2)</span>=1</span><span>log<span>(2x+1)</span>-log<span>(x-2)</span>=1</span></span>Use the quotient property of logarithms, <span><span><span>logb</span><span>(x)</span>−<span>logb</span><span>(y)</span>=<span>logb</span><span>(<span>xy</span>)</span></span><span><span>logb</span><span>(x)</span>-<span>logb</span><span>(y)</span>=<span>logb</span><span>(<span>xy</span>)</span></span></span>.<span><span>log<span>(<span><span>2x+1</span><span>x−2</span></span>)</span>=1</span><span>log<span>(<span><span>2x+1</span><span>x-2</span></span>)</span>=1</span></span>Rewrite <span><span>log<span>(<span><span>2x+1</span><span>x−2</span></span>)</span>=1</span><span>log<span>(<span><span>2x+1</span><span>x-2</span></span>)</span>=1</span></span> in exponential form using the definition of a logarithm. If <span>xx</span> and <span>bb</span> are positive real numbers and <span>bb</span><span>≠≠</span><span>11</span>, then <span><span><span>logb</span><span>(x)</span>=y</span><span><span>logb</span><span>(x)</span>=y</span></span> is equivalent to <span><span><span>by</span>=x</span><span><span>by</span>=x</span></span>.<span><span><span>101</span>=<span><span>2x+1</span><span>x−2</span></span></span><span><span>101</span>=<span><span>2x+1</span><span>x-2</span></span></span></span>Solve for <span>xx</span>Tap for more steps...<span><span>x=<span>218</span></span><span>x=<span>218</span></span></span>Verify each of the solutions by substituting them back into the original equation <span><span>log<span>(2x+1)</span>=1+log<span>(x−2)</span></span><span>log<span>(2x+1)</span>=1+log<span>(x-2)</span></span></span> and solving. In this case, all solutions were found to be valid.<span><span>x=<span>218</span></span><span>x=<span>218</span></span></span>The result can be shown in both exact and decimal forms.Exact Form:<span><span>x=<span>218</span></span><span>x=<span>218</span></span></span>Decimal Form:<span>x=<span>2.625</span></span>
