Question

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Answer 1

$g)\ 10^{3x}=\dfrac{1}{10000}\\ \\ 10^{3x}=\dfrac{1}{10^{4}}\\ \\ 10^{3x}=10^{-4}\\ \\ 3x=-4\\ \\ x=\dfrac{-4}{3}$

$h)\ 10^{1-4x}=0,001\\ \\ 10^{1-4x}=\dfrac{1}{1000}\\ \\ 10^{1-4x}=\dfrac{1}{10^{3}}\\ \\ 10^{1-4x}=10^{-3}\\ \\ 1-4x=-3\\\\ -4x=-3-1\\\\ -4x=-4\\\\ x=\dfrac{-4}{-4}=1$

$i)\ o\ numero\ 8\ esta\ elevado\ a\ quanto?\\ \\ \\ j)\ \dfrac{25^{x}}{5}=1\\ \\ 25^{x}=5\cdot 1\\ \\ \left(5^{2}\right)^{x}=5\\ \\ 5^{2\cdot x}=5^{1}\\ \\ 2x=1\\\\ x=\dfrac{1}{2}$

$k)\ \left(0,25\right)^{x-1}=\left(\dfrac{1}{8}\right)^{1-x}\\ \\ \\ \left(\dfrac{25}{100}\right)^{x-1}=\left(\dfrac{1}{8}\right)^{1-x}\\ \\ \\ \left(\dfrac{1}{4}\right)^{x-1}=\left(\dfrac{1}{8}\right)^{1-x}\\ \\ \\ \left(\dfrac{1}{2^{2}}\right)^{x-1}=\left(\dfrac{1}{2^{3}}\right)^{1-x}\\ \\ \\ \left(2^{-2}\right)^{x-1}=\left(2^{-3}\right)^{1-x}\\ \\ 2^{-2\cdot (x-1)}=2^{-3\cdot (1-x)}\\ \\ -2\cdot (x-1)=-3\cdot (1-x)\\ \\ -2x+2=-3+3x\\ \\ -2x-3x=-3-2\\ \\ -5x=-5\\ \\ x=\dfrac{-5}{-5}=1$

$l)\ 8^{x-4}=4^{x+1}\\ \\ \left(2^{3}\right)^{x-4}=\left(2^{2}\right)^{x+1}\\ \\ 2^{3\cdot (x-4)}=2^{2\cdot (x+1)}\\ \\ 3\cdot (x-4)=2\cdot (x+1)\\ \\ 3x-12=2x+2\\ \\ 3x-2x=2+12\\ \\ x=14$