The correct answer is - The emperor.
In the Byzantine Empire, the emperor was a monarch that had a complete authority, for both the empire's affairs and the religious affairs. So the emperor of the Byzantine Empire had the final word in everything, and apart from being the head of the empire, he was the head of the church as well and dictated the religious activities and politics in the empire, unlike in the west were the pope was in charge of the church activities and politics.
The achievements of the expedition included the European discovery of Alaska, the Aleutian Islands, the Commander Islands, Bering Island, as well as a detailed cartographic assessment of the northern and north-eastern coast of Russia and the Kuril Islands.
Answer with Explanation:
First of all we must understand what actually individual liberty means. Individual liberty means that every person has the right to make choices that they like to go with. This right includes right to express opinion, right to trade, right to live where desired, follow religion that one desires, right to vote and associate, etc.
So the Limited Government (A government that is bound by constitution) to support individual liberty by delivering the above freedom to its people through constitutional amendments, by protecting these rights of the people through implementations of laws and provision of justice.
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>
