1) log за основою одна третя (2х+5)менше 0 2) log за основою одна четверта(3-4х)...

kmetjulia @kmetjulia

June 2022 1 22 Report

1) log за основою одна третя (2х+5)менше 0

2) log за основою одна четверта(3-4х)більше -1

3) log за основою 16(4х+3)більше одної другої

4) lg (12-5х) менше 0

Answers & Comments

konrad509

$\\\log_{\frac{1}{3}}(2x+5)0\\ 2x>-5\\ x>-\frac{5}{2}\\\\ \log_{\frac{1}{3}}(2x+5){\left(\frac{1}{3}\right)}^0\\ 2x+5>1\\ 2x>-4\\ x>-2\\\\ x>-\frac{5}{2} \wedge x>-2\\ \underline{x>-2}$

$\\\log_{\frac{1}{4}}(3-4x)>-1\\ 3-4x>0\\ -4x>-3\\ x\log_{\frac{1}{4}}\left(\frac{1}{4}\right)^{-1}\\ 3-4x$

$\\\log_{16}(4x+3)>\frac{1}{2}\\ 4x+3>0\\ 4x>-3\\ x>-\frac{3}{4}\\\\ \log_{16}(4x+3)>\log_{16}16^{\frac{1}{2}}\\ 4x+3>16^{\frac{1}{2}}\\ 4x+3>4\\ 4x>1\\ x>\frac{1}{4}\\\\ x>\frac{1}{4} \wedge x>-\frac{3}{4}\\ \underline{x>\frac{1}{4}}$

$\\\lg(12-5x)0\\ -5x>-12\\ x$

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Answers & Comments

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