# Exponents and Logarithms

 x3
 x3 = x · x · x
 x-3
 x-3 = 1 / x3
 x1/2
 x1/2 = vx
 vx
 vx = x1/2
 x1/n
 x1/n = nvx
 nvx
 nvx = x1/n
 A general rule for exponents
 xa/b = bvxa = (bvx)a
 the bases for exponents
 -the base-10 system-the natural system
 base-10 system for exponents
 x = 10b
 natural system for exponents
 x = eae ? 2.71828
 the logarithm of a number is equal to…
 its exponent
 the natural logarithm of a number is equal to…
 its exponent
 how to do log for the base-10 rule
 log x = log10(10b) = b
 how to do log for the natural system
 ln x = loge x = loge(ea) = a
 what happens to exponents when numbers are multiplied
 10b · 10c = 10b+ceb · ec = eb+c
 what happens to exponents when numbers go thru division
 10b / 10c = 10b-ceb / ec = eb-c
 what happens to numbers when they are multiplied in the same logarithm
 log(b · c) = log(b) + log(c)
 what happens to numbers when they are divided in the same logarithm
 log(b ? c) = log(b) / log(c)
 what happens to numbers with exponents in a logarithm
 log(axb) = log(a) + b log(x)
 x3
 x3 = x · x · x
 x-3
 x-3 = 1 / x3
 x1/2
 x1/2 = vx
 vx
 vx = x1/2
 x1/n
 x1/n = nvx
 nvx
 nvx = x1/n
 A general rule for exponents
 xa/b = bvxa = (bvx)a
 the bases for exponents
 -the base-10 system-the natural system
 base-10 system for exponents
 x = 10b
 natural system for exponents
 x = eae ? 2.71828
 the logarithm of a number is equal to…
 its exponent
 the natural logarithm of a number is equal to…
 its exponent
 how to do log for the base-10 rule
 log x = log10(10b) = b
 how to do log for the natural system
 ln x = loge x = loge(ea) = a
 what happens to exponents when numbers are multiplied
 10b · 10c = 10b+ceb · ec = eb+c
 what happens to exponents when numbers go thru division
 10b / 10c = 10b-ceb / ec = eb-c
 what happens to numbers when they are multiplied in the same logarithm
 log(b · c) = log(b) + log(c)
 what happens to numbers when they are divided in the same logarithm
 log(b ? c) = log(b) / log(c)
 what happens to numbers with exponents in a logarithm
 log(axb) = log(a) + b log(x)
x

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