I understand that the square root is equal to x^1/2. But what is the cubed root equal to?
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The cube root is x^1/3 so log(cube root of 34) would also be:
1/3 log(34)
1/3 log(34)
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x^(m/n) = n_√x^m ---- where n_√ is the nth root
^--- basic exponent rules
log 3_√34 = log 34^(1/3)
log a^b = b log a
^--- logarithm rules
log 34^(1/3) = 1/3 * log 34
^--- basic exponent rules
log 3_√34 = log 34^(1/3)
log a^b = b log a
^--- logarithm rules
log 34^(1/3) = 1/3 * log 34
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First of all, it's called a "cube root", not a "cubed root".
log (34^(1/3)) = (1/3) log 34
log (34^(1/3)) = (1/3) log 34
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The cube root of x is x^(1/3).
log(34^(1/3)) = (1/3)*log(34)
log(34^(1/3)) = (1/3)*log(34)