What is log 1 & Why?

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Sulabh Mali

Mathematics for JEE Mains/Advanced, XI & XII (All Boards)

log 1 with any base is zero... why? Just because anything power Zero is 1. Obviously base can't be 1 and should be > 0.
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See logarithm of any number is the logarithm to its base e. Here base e redirects as if e^n1=n2 then log(n2)=n1 eg. e^2.0149=7.5 then log(7.5)=2.0149 similarly log(1)=0 because e^0=1.
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Answer: log1 = 0 Proof: 10^0 = 1 converting this exponential equation in to logarithmic equation, log1 to the base 10 = 0.
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Logarithms are designed to study exponential function when we write: a^x = p this is equivalent to writing log p (to base a) = x now we know that any number (except 0) to the power 0 is 1 y^0 = 1 where y is any complex number and is not equal to zero changing the above exponential expression...
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Logarithms are designed to study exponential function when we write: a^x = p this is equivalent to writing log p (to base a) = x now we know that any number (except 0) to the power 0 is 1 y^0 = 1 where y is any complex number and is not equal to zero changing the above exponential expression to logarithmic expression we get log 1 (to base y) =0 base could be anything (except 0) log of 1 is always 0 read less
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Alternative solution Taylor series expansion of log ln(1+x) = x - x^2/2 + x^3/3 -..... put x=0 ln 1 = 0 solution.. This is a proof for natural log... since natural log can be converted to any other logarithms by a multiplication factor of a constant (except of course log 0 is undefined) so log...
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Alternative solution Taylor series expansion of log ln(1+x) = x - x^2/2 + x^3/3 -..... put x=0 ln 1 = 0 solution.. This is a proof for natural log... since natural log can be converted to any other logarithms by a multiplication factor of a constant (except of course log 0 is undefined) so log of 1 to any base will be 0. read less
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Physics becomes quite easy when the curiosity and interest is invoked.

zero
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lakshmi durga d

log(1)=0, u can say by d basic formula log(a/b)=log(a)-log(b)..log(1) can b written as log(1/1)=log(1)-log(1)=0
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