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Question-19194




Question Number 19194 by mondodotto@gmail.com last updated on 06/Aug/17
Answered by allizzwell23 last updated on 06/Aug/17
     (((25)/4) )^(3(x−1)) = ((4/(10)))^(3(5−x))        ((5/2) )^(2(x−1)) = ((2/5))^((5−x))        ((5/2) )^(2(x−1)) = ((5/2))^(−(5−x))     ⇒   2(x−1) = x−5    ∴       x = −3
$$\:\:\:\:\:\left(\frac{\mathrm{25}}{\mathrm{4}}\:\right)^{\mathrm{3}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{4}}{\mathrm{10}}\right)^{\mathrm{3}\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\:\right)^{\mathrm{2}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{2}}{\mathrm{5}}\right)^{\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\:\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\:\right)^{\mathrm{2}\left(\mathrm{x}−\mathrm{1}\right)} =\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{−\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\:\:\Rightarrow\:\:\:\mathrm{2}\left(\mathrm{x}−\mathrm{1}\right)\:=\:\mathrm{x}−\mathrm{5} \\ $$$$\:\:\therefore\:\:\:\:\:\:\:\mathrm{x}\:=\:−\mathrm{3} \\ $$$$ \\ $$$$ \\ $$
Answered by ajfour last updated on 06/Aug/17
(6.25)^((3x−3)) =(0.064)^((5−x))   ⇒    (((25)/4))^(3x−3) =((8/(25)))^(5−x)   ⇒    ((5/2))^(6x−6) =((2/5))^(15−3x)   ⇒     ((5/2))^(6x−6) =((5/2))^(3x−15)   or       6x−6=3x−15           ⇒   x=−3 .
$$\left(\mathrm{6}.\mathrm{25}\right)^{\left(\mathrm{3x}−\mathrm{3}\right)} =\left(\mathrm{0}.\mathrm{064}\right)^{\left(\mathrm{5}−\mathrm{x}\right)} \\ $$$$\Rightarrow\:\:\:\:\left(\frac{\mathrm{25}}{\mathrm{4}}\right)^{\mathrm{3x}−\mathrm{3}} =\left(\frac{\mathrm{8}}{\mathrm{25}}\right)^{\mathrm{5}−\mathrm{x}} \\ $$$$\Rightarrow\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{6x}−\mathrm{6}} =\left(\frac{\mathrm{2}}{\mathrm{5}}\right)^{\mathrm{15}−\mathrm{3x}} \\ $$$$\Rightarrow\:\:\:\:\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{6x}−\mathrm{6}} =\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{3x}−\mathrm{15}} \\ $$$$\mathrm{or}\:\:\:\:\:\:\:\mathrm{6x}−\mathrm{6}=\mathrm{3x}−\mathrm{15} \\ $$$$\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\mathrm{x}=−\mathrm{3}\:. \\ $$

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