LOGARITHMS

LOGARITHMS

The logarithms of any number of a given base is equal to which the base should be raised to obtain the given number.

We write "the number of 2s we need to multiply to get 8 is 3" as:

log₂(8) = 3

then this is read as "log base 2 of 8 is 3"

PROPERTIES OF LOGARITHMS:

• logx+logy=log(xy)

• logx-logy=log(x/y)

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• log_b b = 1

• log_b 1 = 0

Example:

If logx+logy=log(x+y) then find the relation between x and y.

⇒logx+logy=log(x+y)

or

⇒log(xy)=log(x+y)

or

⇒xy=(x+y)

Example:

If  logx+log(4x)=log4 then find the value of x?

⇒logx+log(4x)=log4

⇒logx+log(4x)=log4

⇒log(4x²)=log4

⇒4x²=4

⇒x²=1

⇒x=±1

from this x=-1 and x=1

but x=1 is the only solution because negative of log is not defined.

Example:

If  logx-log(4)=log2 then find the value of x ?

⇒logx-log(4)=log2

⇒logx-log(4x)=log4

⇒log(x/4)=log4

⇒(x/4)=4

⇒x=16

What is the value of log₆ (1296)?

let y=log₆1296

y=log₆6⁴

y=4log₆6

y=4log6/log6

y=4

Work for you

1. Find x, if log2x+logx=log8

2. Find the relation between x,y and z, if 2logx+logy=logz

3. Find x, if 2logx-log4=log4