log 3 Base 4 equal to log 4 by log 3
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Simply change the base using the formula.
logbase4(3)=logbase2(3)/logbase2(4)
logbase2(4)=2
Now because you’re halving logbase2(3), the number of times 2 can multiply itself to get 3 has been also halved. rt3 also requires half the number, as two rt3, multiplied together is 3, and the numbers of letting 2 add up to logbase2(3).
That’s how you convert logbase4(3) to logbase2(√3).
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logbase4(3)=logbase2(3)/logbase2(4)
logbase2(4)=2
Now because you’re halving logbase2(3), the number of times 2 can multiply itself to get 3 has been also halved. rt3 also requires half the number, as two rt3, multiplied together is 3, and the numbers of letting 2 add up to logbase2(3).
That’s how you convert logbase4(3) to logbase2(√3).
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1
Let, log 3 to the base 4= x
Therefore, 3=4^x=2^(2x)=(2^x)^2, taking sware root on both side.
√3=2^x
Taking log base 2 on both side,
Log √3 to the base 2=log 2^x to the base 2
Log √3 to the base 2=x×log 2 to the base 2=x*1=x
Log √3 to the base 2= log 3 to the base 4
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