Question

Question #484ea

Answer 1

`x=(1+-sqrt65)/8=1.13`

Explanation:

`ln(x+4)=lnx^2+ln(4)`-> Use property `log_ba^x=xlog_ba`
`ln(x+4)=ln(4x^2)`->Use property `log_b(xy)=log_bx+log_by`
`ln(x+4)-ln(4x^2)=0`-> Put everything on one side
`ln((x+4)/(4x^2))=0`->Use property `log_b(x/y)=log_bx-log_by`
`10^0 = (x+4)/(4x^2)`-> use definition `y=logx iff 10^y=x`
`1=(x+4)/(4x^2)`
`4x^2=x+4`
`4x^2-x-4=0`
`x=(1+-sqrt(1-4(4)(-4)))/8`
`x=(1+-sqrt65)/8=1.13 or -0.88`