Решите неравенство поэтапно:. Created by Bergamotte. matematika-ru

Решите неравенство поэтапно:...

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4*(1/4)^x+(1/4)^x<80
5*(1/4)^x<80
(1/4)^x<80/5
(1/4)^x<16
(1/4)^x<(1/4)^-2
основание меньше 1,знак меняется
x>-2
x∈(-2;∞)

1 votes Thanks 1

IrkaShevko

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$( \frac{1}{4} )^{x-1}(1+ \frac{1}{4} ) \ \textless \ 80\\
( \frac{1}{4} )^{x-1} \ \textless \ \frac{80*4}{5} \\
( \frac{1}{4} )^{x-1} \ \textless \ 4^3 = ( \frac{1}{4} )^{-3}\\
x-1 \ \textgreater \ -3\\
x\ \textgreater \ -2$

Поменяли знак на противоположный, т.к. основание (1/4) меньше 1 по модулю

1 votes Thanks 0

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