Question 1

30+ Points!!!
5. Solve the following inequalities.
a) 2 log3x – 2 logx3 -3 <0

Question 2

Answer:

I answered your last question also

2 log3x – 2 logx3 -3 <0

$\mathrm{Subtract\:}2\log ^3\left(x\right)\mathrm{\:from\:both\:sides}$

$2\log ^3\left(x\right)-2logx^3-3-2\log ^3\left(x\right)<0-2\log ^3\left(x\right)$

$\mathrm{Simplify}$

$-2logx^3-3<-2\log ^3\left(x\right)$

$\mathrm{Add\:}3\mathrm{\:to\:both\:sides}$

$-2logx^3-3+3<-2\log ^3\left(x\right)+3$

$\mathrm{Simplify}$

$-2logx^3<-2\log ^3\left(x\right)+3$

$Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)$

$\left(-2logx^3\right)\left(-1\right)>-2\log ^3\left(x\right)\left(-1\right)+3\left(-1\right)$

$\mathrm{Simplify}$

$2lx^3og>2\log ^3\left(x\right)-3$

$\mathrm{Divide\:both\:sides\:by\:}2lx^3o;\quad \:l>0$

$(2lx^3og)/(2lx^3o)>(2\log ^3\left(x\right))/(2lx^3o)-(3)/(2lx^3o);\quad \:l>0\\$

$\mathrm{Simplify}$

$g>(2\log ^3\left(x\right)-3)/(2lx^3o);\quad \:l>0$

Explanation:

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