HL Math help please
Basically i am preparing for an exam tomorrow and i can't figure out how to solve these 3 problems. Could someone who knows math please solve them quickly. I would be really grateful.
1) a) If log(a - b) = logs - logb, find an expression for a in terms of b, stating any restrictions on b.
b) a2 + b2 – 2ab = 4 and ab = 4, where a > 0, b > 0, find the value of 2log20(a+b)
2) find the maximum domain of the function f(x) = 1/(ln(lnx))
3) Let f(x)=2e-x + 3, x E R
Find:
a) f(-1)
b) f-1(4) (if possible use two methods for this one)
If someone could solve these for me and show me the process that would be awesome.
1) a) If log(a - b) = logs - logb, find an expression for a in terms of b, stating any restrictions on b.
b) a2 + b2 – 2ab = 4 and ab = 4, where a > 0, b > 0, find the value of 2log20(a+b)
2) find the maximum domain of the function f(x) = 1/(ln(lnx))
3) Let f(x)=2e-x + 3, x E R
Find:
a) f(-1)
b) f-1(4) (if possible use two methods for this one)
If someone could solve these for me and show me the process that would be awesome.
Original post by math97
Basically i am preparing for an exam tomorrow and i can't figure out how to solve these 3 problems. Could someone who knows math please solve them quickly. I would be really grateful.
1) a) If log(a - b) = logs - logb, find an expression for a in terms of b, stating any restrictions on b.
1) a) If log(a - b) = logs - logb, find an expression for a in terms of b, stating any restrictions on b.
Is logs a typo? I'm guessing that should be loga. If so, then recall the quotient rule of logs: loga - logb = log(a/b). Work your way from there.
b) a2 + b2 – 2ab = 4 and ab = 4, where a > 0, b > 0, find the value of 2log20(a+b)
Factorise a2 + b2 - 2ab and recall the power law of logs: alogx = logxa. Might be slightly tricky and require a bit more thinking, this one.
2) find the maximum domain of the function f(x) = 1/(ln(lnx))
Not sure on this one, because if I haven't made a mistake there is no upper limit to the domain of f(x).
3) Let f(x)=2e-x + 3, x E R
Find:
a) f(-1)
Find:
a) f(-1)
b) f-1(4)
Let f(x) = y (so y=2e-x). Find f-1 by swapping x and y and rearranging to make y the subject, then sub in 4 for x.
(edited 11 years ago)
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