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Please help with logarithmic equation!
- Thread starter Xonian
- Start date
Please show us what you have tried so far. That way we can pinpoint your error and help you not repeat the error next time.ln(3√x)= √(ln x)
Please help me solve this. I've spent hours trying and I just can't get it. Thanks!:razz:
Please show us what you have tried so far. That way we can pinpoint your error and help you not repeat the error next time.
Ok. I did as follows:
1. ln3 + ln√x = √(ln x)
2. ln3 + .5lnx = √(ln x)
3. 2ln3 + lnx = 2√(ln x)
4. 2.2 + lnx = 2√(ln x)
5. 4.84 + (lnx)^2 = 4lnx
6. (lnx)^2 - 4lnx = -4.84
7. lnx - 4 = -4.84/lnx
From here, I had no idea on how to proceed.
Ok. I did as follows:
1. ln3 + ln√x = √(ln x)
2. ln3 + .5lnx = √(ln x)
3. 2ln3 + lnx = 2√(ln x)
4. 2.2 + lnx = 2√(ln x)
5. 4.84 + (lnx)^2 = 4lnx ===> Wrong
6. (lnx)^2 - 4lnx = -4.84
7. lnx - 4 = -4.84/lnx
From here, I had no idea on how to proceed.
First, going from step 4 to step 5 is incorrect. \(\displaystyle (2.2+lnx)^2 \ne (2.2)^2 + (lnx)^2\). That being said, this equation has no real solutions. Take a look at this:
http://www.wolframalpha.com/input/?i=ln(3x^.5)=(lnx)^.5
D
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.Ok. I did as follows:
1. ln3 + ln√x = √(ln x)
2. ln3 + .5lnx = √(ln x)
3. 2ln3 + lnx = 2√(ln x)
4. 2.2 + lnx = 2√(ln x)
5. 4.84 + (lnx)^2 = 4lnx → This is incorrect. It should be
5. 4[ln(3)]2+ [ln(x)]2 + 4[ln(3)]*ln(x) = 4ln(x)
Substitute
u = ln(x)
6. 4[ln(3)]2+ 2 + [4*ln(3)-1]*ln(x) = 0
This is a quadratic equation → solve for u → solve for x
From here, I had no idea on how to proceed.