Log 2 Square root of 2

Sorry I couldnt make it look right, but the first 2 is the base and the second is the square root of 2, can anyone solve it?

Also can anyone express this, In 2x + 3(In x - In y), as a single logarithm?
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2 to the power of what gives you square root two? a square root sign means an exponent of 1/2. so therefore 2 to the power of 1/2 gives you square root 2. your answer is 1/2.

the other one, uses laws like logA + logB = log (AB)
logA-logB=logA/B
3logA=long(A^3)

so brackets first: In 2x + 3(In x - In y)

lnx-lny=ln(x/y)

and with the exponent
3ln(x/y)=ln[(x/y)^3]

ln[2x(x/y)^3]
Last edited by allfallsdown at Nov 13, 2008,

Second question:

ln 2x + 3(ln x -ln y) = ln 2x + 3 ln (xy) = ln 2x + ln (xy)^3...you can finish this off
2^unknown=root2

ln 2x[(ln x/ln y)^3]

you can simplify from there
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Ahh ok thanks allfallsdown, smb, and slash, I knew that, i just wansnt using my head lol Thanks!
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