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Question

Tìm x biết:

a, $81^{-2x}.27^x=9^5$

b, $2^x+2^{x+3}=144$

c, $2^{x-1}+5.2^{x-2}=7.32$

Lưu Hạ Vy · Accepted Answer

a) $81^{-2x}.27^x=9^5$

$\Rightarrow\left(3^4\right)^{-2x}.\left(3^3\right)^x=3^{10}$

$\Rightarrow3^{-8x}.3^{3x}=3^{10}$

$\Rightarrow3^{-5}=3^{10}$

$\Rightarrow-5x=10$

$\Rightarrow x=-2$

Vậy $x=-2$

b) $2^x+2^{x+3}=144$

$\Rightarrow\left(1+2^3\right).2^x=144$

$\Rightarrow\left(1+8\right).2^x=144$

$\Rightarrow9.2^x=144$

$\Rightarrow2^x=16$

$\Rightarrow x=4$

Vậy $x=4$

c) $2^{x-1}+5.2^{x-2}=7.32$

$\Rightarrow\left(2+5\right).2^{x-2}=244$

$\Rightarrow7.2^{x-2}=244$

$\Rightarrow2^{x-2}=32$

$\Rightarrow x-2=5$

$\Rightarrow x=7$

Vậy $x=7$Câu trả lời: a) $81^{-2x}.27^x=9^5$