Question

equações exponenciais
e-) (0,001)^x=1000
f-)(1/100)^2x=0,0001
g-) (1/3)^x²-10=1/727
h-)(0,5)x=4^1-3x

Answer 1

e)
$(0,001)^x=1000 \\ 10^{-3x}=10^3 \\ -3x=3 \\ 3x=-3 \\ x=-3\div3 \\ x=-1$

f)
$( \frac{1}{100} )^{2x}=0,0001 \\ \\ (10^{-2})^{2x}=10^{-4} \\ \\ 10^{-4x}=10^{-4} \\ -4x=-4 \\ 4x=4 \\ x=4\div4 \\ x=1$


g)
$( \frac{1}{3} )^{ x^{2} -10}= \frac{1}{729} \\ \\ 3^{-( x^{2} -10)}=3^{-5} \\ \\ - x^{2} +10=-5 \\ - x^{2} =-5-10 \\ -x^2=-15 \\ x^2=15 \\ x=\pm \sqrt{15}$


h)
$(0,5)^x=4^{1-3x} \\ \\ ( \frac{5}{10} )^x=4^{1-3x} \\ \\ ( \frac{1}{2} )^x=4^{1-3x} \\ \\ 2^{-x}=2^{2(1-3x)} \\ -x=2-6x \\ -x+6x=2 \\ 5x=2 \\ \\ x= \frac{2}{5}$