Log (10-4x) = log (10-3x)

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asked Feb 28, 2015 85.1k views

2 votes

Log (10-4x) = log (10-3x)

Mathematics
high-school

Siame asked

by Siame

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2 Answers

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$\log (10-4x) = \log (10-3x) \\ D:10-4x>0 \wedge 10-3x>0\\ D:4x<10 \wedge 3x<10\\ D:x<2.5 \wedge x<3(1)/(3)\\ D:x<2.5\\ 10-4x=10-3x\\ x=0$

Ardee Aram answered Mar 1, 2015

by Ardee Aram

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3 votes

$D:\\10-4x > 0\ \wedge\ 10-3x > 0\\-4x > -10\ \vee\ -3x > -10\\\\x < (10)/(4)\ \wedge\ x < (10)/(3)\\\\x < 2(1)/(2)\ \wedge\ x < 3(1)/(3)\\\\x\in(-\infty;\ 2(1)/(2))$

$log(10-4x)=log(10-3x)\iff10-4x=10-3x\\\\-4x+3x=10-10\\\\-x=0\ \ \ /\cdot(-1)\\\\x=0\in D\\\\Solution:x=0$

Akhalsa answered Mar 6, 2015