3^2x+6=2^x+3 5^x-2=4^2x-4 Эти как решить...

mragzam19 @mragzam19

August 2022 1 12 Report

3^2x+6=2^x+3

5^x-2=4^2x-4
Эти как решить

Answers & Comments

Universalka

Verified answer

$1)3^{2x+6}=2^{x+3} \\\\(3^{2})^{x+3}=2^{x+3}\\\\9^{x+3}=2^{x+3}|:2^{x+3}>0 \\\\\frac{9^{x+3} }{2^{x+3} }=\frac{2^{x+3} }{2^{x+3} }\\\\(\frac{9}{2})^{x+3}=1\\\\(\frac{9}{2})^{x+3}=(\frac{9}{2})^{0}\\\\x+3=0\\\\x=-3$

$2)5^{x-2}=4^{2x-4}\\\\5^{x-2}=(4^{2})^{x-2}\\\\5^{x-2} =16^{x-2} |:16^{x-2}>0\\\\(\frac{5}{16})^{x-2}=1\\\\(\frac{5}{16})^{x-2}=(\frac{5}{16})^{0}\\\\x-2=0\\\\x=2$

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