Найдите решение уравнения. Created by Lana2201. algebra-ru

Найдите решение уравнения...

Lana2201 @Lana2201

July 2022 1 7 Report

Найдите решение уравнения

Answers & Comments

NNNLLL54

Verified answer

$log_{1/2}^2(4x)+log_2\frac{x^3}{8}=8\; \; \; ,\; \; \; ODZ:\; x>0\\\\\star \; \; log^2_{1/2}(4x)=\Big (log_{1/2}(4x)\Big )^2=\Big (-log_2(4x)\Big )^2=(-1)^2\cdot \Big (log_24+log_2x\Big )^2=\\\\=(2+log_2x)^2=4+4log_2x+log_2^2x\; ;\\\\\star \; \; log_2\frac{x^3}{8}=log_2(\frac{x}{2})^3=3\, (log_2x-log_22)=3log_2x-3\; ;\\\\4+4\, log_2x+log_2^2x+3log_2x-3=8\\\\log_2^2x+7\, log_2x-7=0\; \; ,\; \; \; D=7^2+4\cdot 7=77\; ,\\\\log_2x=\frac{-7-\sqrt{77}}{2}\; \; ,\; \; \log_2x=\frac{-7+\sqrt{77}}{2}$

$x_1=2^{\frac{-7-\sqrt{77}}{2}}=\sqrt{2^{-7-\sqrt{77}}} \; \; ,\; \; x_2=2^{\frac{-7+\sqrt{77}}{2}}=\sqrt{2^{-7+\sqrt{77}}}$

2 votes Thanks 1

Answers & Comments

Verified answer

pozhalujsta pomogite763084fd3eeefaf1a127f00d4ab72ee2 24269

ochen nuzhna pomoshreshite pozhalujstab7b0f0bd307dc98b795454cd322481cb 59019

pomogite najti znachenie3a667bf7599e6b185ea7ce14501785f5 74182

pomogite pozhalujsta zaranee ogromnoe spasibo5bc52f5b6e6c8027aed4a9c9c43a0900 75207

pomogite pozhalujsta uprostit vyrazhenie pri

ochen nuzhna pomosh spasibo zaranee475075c49cf4a869363847cf44089c64 85219

pomogite reshit uravnenie805a7f53fd768115c7dfa198b4c1ce81 16640

uprostit vyrazhenie pri

reshit sistemu uravnenij8aca1b8007b267f3e9e8fd0ca6b034b1 36078

рекомендуемые вопросы

Helpful Links

Helpful Social