Question

решите показательные уравнения:
1) 3^x-1+ 3^x-2 + 3^x-3=13
2)5^5-x=100 * 2^[-5
3)5^x-1 + 5*0.2^x-2-26

Answer 1

$1)3^{x-1}+3^{x-2}+3^{x-3}=13<=>3^{x-3}(3^2+3+1)=13<=>13*3^{x-3}=13<=>\\<=>3^{x-3}=1=>x=3\\2)5^{5-x}=100*2^{-5+x}<=>\frac{1}{5^{x-5}}=25*2^{x-3} <=>\\<=>1=25*5^{x-5}*2^{x-3}<=>1=10^{x-3}=>x=3\\3)5^{x-1}+5*0,2^{x-2}-26=0<=>5^{x-1}+5^{-x+3}-26=0\\5^x=t=>\frac{t}{5} +\frac{5^3}{t} -26=0<=>t^2-26*5t+5^4=0<=>\\<=>(t-5)(t-125)=0\\5^x=5=>x=1\\5^x=125=>x=3$