Logarithms ALPHA Maths Module : Pipeng Free Online Software

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Pipeng Free Online Software : Logarithms ALPHA Maths Module

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Pipeng : Maths Algebra : Natural Logarithms Base 10 Logarithms And Arbitrary Base Logarithms ALPHA Maths Homework Module

Logarithms ALPHA Maths Module

Description : Maths Algebra : Natural Logarithms Base 10 Logarithms And Arbitrary Base Logarithms

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ALPHA : Algebra : Logarithm 01 : Natural Base E Logs And Inverse Logs Or Exponentials : ALPHA Maths Homework Exercise

Description : Natural base e logs and inverse logs or exponentials.

Discussion : Natural logs are to the base e. The inverse of natural log is the exponential.

The homework exercise has 2 questions.

log x

The equations are :

logx = log(x)

x = e^logx

ALPHA : Algebra : Logarithm 02 : Base 10 Logs And Inverse Logs Or Powers : ALPHA Maths Homework Exercise

Description : Base 10 logs and inverse logs or powers.

Discussion : Base 10 logs are to base 10 rather than base e. The inverse of a base 10 log is a power of 10.

The homework exercise has 2 questions.

log x

The equations are :

logx = log10(x)

x = 10^logx

ALPHA : Algebra : Logarithm 03 : Convert Between Base 10 Logs And Natural Logs : ALPHA Maths Homework Exercise

Description : Converting between base 10 logs and natural logs.

Discussion : Convert between natural logs and base 10 logs by multiplying or dividing by base 10 log of E or natural log of 10.

The homework exercise has 2 questions.

base 10 log x

natural log x

The equations are :

log10(x) = log(x) / log(10) = log(x) log10(E)

log(x) = log10(x) / log10(E) = log10(x) log(10)

log10(E) = 1 / log(10)

ALPHA : Algebra : Logarithm 04 : Convert Between Arbitrary Base Logs And Natural Logs : ALPHA Maths Homework Exercise

Description : Convert between arbitrary base logs and natural logs.

Discussion : Convert between arbitrary base logs and natural logs by multiplying or dividing by the natural log of the base.

The homework exercise has 3 questions.

base b log x

base b

The equations are :

logb(x) = log(x) / log(b)

x = e^{logb(x) log(b)}

b = e^{log(x) / logb(x)}

ALPHA : Algebra : Logarithm 05 : Adding Logs : Multiplying Numbers : ALPHA Maths Homework Exercise

Description : Adding logs : multiplying numbers.

Discussion : The log of a times b equals the sum of the logs.

The homework exercise has 3 questions.

log(a b)

log(a)

The equations are :

log(a b) = log(a) + log(b)

a b = e^{log(a) + log(b)}

a = e^{log(a b) - log(b)}

b = e^{log(a b) - log(a)}

where

a b = numbers

ab = a b

loga logb = natural log of a and b

logab = natural log of a b

ALPHA : Algebra : Logarithm 06 : Subtracting Logs : Dividing Numbers : ALPHA Maths Homework Exercise

Description : Subtracting logs : dividing numbers.

Discussion : The log of a divided by b equals the log of a minus the log of b.

The homework exercise has 3 questions.

a / b

The equations are :

log(a / b) = log(a) - log(b)

a / b = e^{log(a) - log(b)}

a = e^{log(a / b) + log(b)}

b = e^{log(a) - log(a / b)}

where

a b = numbers

ab = a / b

loga logb = natural log of a and b

logab = natural log of a / b

ALPHA : Algebra : Logarithm 07 : Multiplying Or Dividing Logs : Powers Or Roots Of Numbers : ALPHA Maths Homework Exercise

Description : Multiplying or dividing logs : powers or roots of numbers.

Discussion : Multiply a log by an index n to calculate the log of the nth power of x. Divide a log by an index n to calculate the log of the nth root of x.

The homework exercise has 3 questions.

nth power

nth root

index n

The equations are :

nx = e^{n logx}

x = e^{lognx / n<.esup>}

n = lognx / logx

where

x = number

nx = nth power of x

n = power

logx = log x

lognx = log of nth power of x

ALPHA : Algebra : Logarithm 08 : Negative Logs : Inverse Of Numbers : ALPHA Maths Homework Exercise

Description : Negative logs : inverse of numbers.

Discussion : Calculate the inverse of a number from the negative log.

The homework exercise has 2 questions.

inverse

The equations are :

ix = e^-logx

x = e^-logix

where

x = number

ix = inverse of x

logx = log x

logix = log of inverse of x

ALPHA : Algebra : Logarithm 09 : Inverse Logs : Reverse Number And Base : ALPHA Maths Homework Exercise

Description : Inverse logs : reverse number and base.

Discussion : Taking the inverse of a log reverses or switches the base and the number.

The homework exercise has 2 questions.

logb(10)

logb(E)

The equations are :

logb(10) = 1 / log10(b)

logb(E) - 1 / log(B)

where

b = logarithm base

logb() = log to base b

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