Can someone explain to me how to solve for x in this example?

 

ln(x-2)=3

 

 

Also, is there a difference between ln, lg, and log or do they all mean the same thing?

 

Thanks

ln is just log base e right? so you just switch the formula around so that it is [math]e^3=x-2[/math] then solve for x

 

[math]x=e^3+2[/math]

ln is log base e. It's just used so often in natural sciences that it has it's own symbol.

 

ln y = x, is the same thing as saying: e^x = y

lg is base 10 and log alone is moot: mathematicians would say it is base e, some applied scientists that it is base 10 and others that it is base 2, depending on the context. If you're doing engineering it is safest to assume that log means base 10 unless specified otherwise, and if doing maths then it is log base e.

 

Note that base e is the natural one to do maths in for reasons you'll meet in analysis later, just as the natural unit for angles is the radian and not the degree.