Subject: Integration and Equations

Question: Hi I've got a question concerning Integration and equations. I'm not sure what symbol to use for the squigly line for integration so I've just used the "&" key and I've put the definite limits directly after the "&" symbol separated by commas, the top one first and the bottom one second. Ok the question is:

If a>0

&b,0 1/(1+x)dx = 1/2&a,0 1/(1+x)dx

Express "b" in terms of "a"

Here's the work I've done so far

Log[1+x] = 1/2(Log[1+x])

Log[1+b]-Log[1+0]=1/2Log[1+a]-1/2Log[1+0]

Log[1+b]=1/2Log[1+a]

At this point I'm not sure if I can divide accross by Log or whether I have to bring the Logs over to one side and procede with Log subtraction. Either way I don't get the right answer which is: b=(1+a)²-1

Please help me with this one, Thanks

At the point where you are stuck, Log[1+b]=1/2Log[1+a], use the identity cLog[t] = Log[t ^c] on the second factor.