Answer:
The USS Maine explodes and sinks in Havana Harbor on Feb. 15, 1898, killing 266 American sailors. Pressured by the "yellow press," the U.S. declares war on Spain on April 25, 1898, resulting in the deaths of thousands and the collapse of the Spanish empire.
Explanation:
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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>
