Question

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

Answer 1

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: