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Exponents and Logarithms
Part of the Math Review
38
Chemistry
Undergraduate 4
01/05/2017
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Term
x3
 Definition
x3 = x · x · x
Term
x-3
 Definition
x-3 = 1 / x3
Term
x1/2
 Definition
x1/2 = √x
Term
√x
 Definition
√x = x1/2
Term
x1/n
 Definition
x1/n = n√x
Term
n√x
 Definition
n√x = x1/n
Term
A general rule for exponents
 Definition
xa/b = b√xa = (b√x)a
Term
the bases for exponents
 Definition
-the base-10 system
-the natural system
Term
base-10 system for exponents
 Definition
x = 10b
Term
natural system for exponents
 Definition
x = ea e ≈ 2.71828
Term
the logarithm of a number is equal to...
 Definition
its exponent
Term
the natural logarithm of a number is equal to...
 Definition
its exponent
Term
how to do log for the base-10 rule
 Definition
log x = log10(10b) = b
Term
how to do log for the natural system
 Definition
ln x = loge x = loge(ea) = a
Term
what happens to exponents when numbers are multiplied
 Definition
10b · 10c = 10b+c eb · ec = eb+c
Term
what happens to exponents when numbers go thru division
 Definition
10b / 10c = 10b-c eb / ec = eb-c
Term
what happens to numbers when they are multiplied in the same logarithm
 Definition
log(b · c) = log(b) + log(c)
Term
what happens to numbers when they are divided in the same logarithm
 Definition
log(b − c) = log(b) / log(c)
Term
what happens to numbers with exponents in a logarithm
 Definition
log(axb) = log(a) + b log(x)
Term
x3
 Definition
x3 = x · x · x
Term
x-3
 Definition
x-3 = 1 / x3
Term
x1/2
 Definition
x1/2 = √x
Term
√x
 Definition
√x = x1/2
Term
x1/n
 Definition
x1/n = n√x
Term
n√x
 Definition
n√x = x1/n
Term
A general rule for exponents
 Definition
xa/b = b√xa = (b√x)a
Term
the bases for exponents
 Definition
-the base-10 system
-the natural system
Term
base-10 system for exponents
 Definition
x = 10b
Term
natural system for exponents
 Definition
x = ea e ≈ 2.71828
Term
the logarithm of a number is equal to...
 Definition
its exponent
Term
the natural logarithm of a number is equal to...
 Definition
its exponent
Term
how to do log for the base-10 rule
 Definition
log x = log10(10b) = b
Term
how to do log for the natural system
 Definition
ln x = loge x = loge(ea) = a
Term
what happens to exponents when numbers are multiplied
 Definition
10b · 10c = 10b+c eb · ec = eb+c
Term
what happens to exponents when numbers go thru division
 Definition
10b / 10c = 10b-c eb / ec = eb-c
Term
what happens to numbers when they are multiplied in the same logarithm
 Definition
log(b · c) = log(b) + log(c)
Term
what happens to numbers when they are divided in the same logarithm
 Definition
log(b − c) = log(b) / log(c)
Term
what happens to numbers with exponents in a logarithm
 Definition
log(axb) = log(a) + b log(x)
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