Mathematics: Solve the logarthmic equations. round answers to the nearest hundredth. log2(x - 6) + log2(x - 4) = log2 x x = 8, 3 x = 8 no solution

You would have to graph it if that !...

Solve the logarthmic equations. round answers to the

Ответ:

skateboardb718

13.03.2022

$\text{The domain:}\\x-6 \ \textgreater \ 0\ \wedge\ x-4 \ \textgreater \ 0\ \wedge\ x \ \textgreater \ 0\\x \ \textgreater \ 6\ \wedge\ x \ \textgreater \ 4\ \wedge\ x\ \textgreater \ 0\\\\D:x\in(6;\ \infty)\\\\\log_2(x-6)+\log_2(x-4)=\log_2x\\\\\log_2[(x-6)(x-4)]=\log_2x\iff(x-6)(x-4)=x\\\\x^2-4x-6x+24=x\\\\x^2-10x+24=x\ \ \ |-x\\\\x^2-11x+24=0\\\\x^2-8x-3x+24=0\\\\x(x-8)-3(x-8)=0\\\\(x-8)(x-3)=0\iff x-8=0\ \vee\ x-3=0\\\\x=8\in D\ \vee\ x=3\notin D\\\\\text{}\ x=8$

0,0(0 оценок)

Solve the logarthmic equations. round answers to the nearest hundredth. log2(x - 6) + log2(x - 4) = log2 x x = 8, 3 x = 8 no solution

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question