Question

say the rules of logarithms​

Answer 1

Answer:

Logarithm Rules

The base b logarithm of a number is the exponent that we need to raise the base in order to get the number.

Logarithm definition

Logarithm rules

Logarithm problems

Complex logarithm

Graph of log(x)

Logarithm table

Logarithm calculator

Logarithm definition

When b is raised to the power of y is equal x:

b y = x

Then the base b logarithm of x is equal to y:

logb(x) = y

For example when:

24 = 16

Then

log2(16) = 4

Logarithm as inverse function of exponential function

The logarithmic function,

y = logb(x)

is the inverse function of the exponential function,

x = by

So if we calculate the exponential function of the logarithm of x (x>0),

f (f -1(x)) = blogb(x) = x

Or if we calculate the logarithm of the exponential function of x,

f -1(f (x)) = logb(bx) = x

Natural logarithm (ln)

Natural logarithm is a logarithm to the base e:

ln(x) = loge(x)

When e constant is the number:

e=\lim_{x\rightarrow \infty }\left ( 1+\frac{1}{x} \right )^x = 2.718281828459...

or

e=\lim_{x\rightarrow 0 }\left ( 1+ \right x)^\frac{1}{x}

 

See: Natural logarithm

Inverse logarithm calculation

The inverse logarithm (or anti logarithm) is calculated by raising the base b to the logarithm y:

x = log-1(y) = b y

Logarithmic function

The logarithmic function has the basic form of:

f (x) = logb(x)

Explanation:

Answer 2

Answer:

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