Product of log problem

[Dale10101]

Thanks for any help.

 

[Dale10101]

Thanks

well you've got problems right out of the gate.

let's start with

\(\displaystyle \ln(x+3)\ln(2x+1)\)

\(\displaystyle \ln(x+3)\ln(2x+1)=\ln\left((2x+1)^{\ln(x+3)}\right)\)

and at \(\displaystyle x=4\) this becomes

\(\displaystyle \ln\left((2\cdot 4 + 1)^{\ln(4+3)}\right)=\ln(9^{\ln(7)})\)

punch this into your calculator or whatever and you get 4.2756 etc...

note for grins and giggles that also

\(\displaystyle \ln(x+3)\ln(2x+1)=\ln\left((x+3)^{\ln(2x+1)}\right)\)

at \(\displaystyle x=4\) this becomes

\(\displaystyle \ln(7^{\ln(9)})=4.2756...\)

Thanks for your correction, I did not keep track of what was being transformed, i.e the argument and not the function. Could I trouble you for one further bit of information ... the name of the function which gives a numeric estimation of log(x)log(y), some W(x,y). I have tried to find it on the internet but cannot locate it? Thanks.