Solving Logarithmic Function Examples

Definition of solving Logarithmic function with examples:

The inverse of the exponential function is known as the Logarithmic function.    

Basic Logarithmic rules for solving Logarithmic function example         

If a, m and n are positive numbers and a is not equal to 1, then
Loga (mn)=  Loga m+Logan


If m, n and a are positive numbers and a is not equal to 1, then
Loga(m/n)=Loga(m)- Loga (n)


If a and m are positive numbers, a is not equal to 1 and n is a real number, then
Loga(mn)= n Log a m


If m, n and p are positive numbers and n is not equal to 1,  and p is not equal to 1, then
Log nm= (Log lm) (Logl n)

If m and n are two positive numbers other than 1, then
Logn m= 1/(Logm  n)

Special rules for solving Logarithmic function:

blogb a  = a

Log a 1 = 0

Loga a   = 1

Solving Logarithmic Function with Examples

Convert  Logarithmic form to exponential form:

log2  8 = (1/3)

The equivalent  exponential form is (2)(1/3)  = 8

log8 64 = 2

The equivalent  exponential form  is    (8)2 = 64

log7 (1/343) = –3

The equivalent  exponential form  is  1/343 = (7)-3

log3  27= 3

The equivalent  exponential form  is  27 = (3)3

Convert  exponential form to Logarithmic form:

Solving 729 = (9)(1/3)

The equivalent Logarithmic form is

log9 (729) = 1/3

Solving 1/6 = (6)-1

The equivalent Logarithmic form is

-1= log6(1/6)

(25)1/2=5

The equivalent Logarithmic form is

log25  5=(1/2)

(216)(1/3) =6

The equivalent Logarithmic form is

log 216  6 = (1/3)

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Evaluate for Solving Logarithmic Function with Examples:

Solve log 15  225

Solution:

Let x = log 15  225

then   15x  = 225

15x =(15)2

therefore x=2.

Solve log 4(1/64)

Solution:

Let x =log4 (1/64)

4x =(1/43)

4x = 4-3

therefore x=-3

Solve the equations:

log x 1000 = 3

x3 = 1000

x3 =103

x=10

x = log(1/6)  216

(1/6)x  = (6)3

(1/6)x = (1/6)-3

x = -3

Prove that the solving logarithmic function :

log 4 7 * Log 10 25 * Log 4 9 * log5  75 = 4

( Log4 7 * Log 4 9) + (Log 10 25 * Log 10 75)

Log 4 (7 + 9) + (Log 10(25 + 75))

Log 4 (16) + Log10 (100)

Log 4 (4)2  + Log 10 (10)2

2 Log 44  + 2Log 10  10

2(1) + 2(1)

= 2 + 2 = 4