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)