What is logarithm in math - Applied Mathematics | questions on logarithm

logarithm

• table of content
• basic information
• exponentail
• stander formate of logarithm
• addition of logarithm
• subtraction in logarithm
• Logarithm Quiz

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Exponential

exponantial function means terums which forme is f(x)= `a^x` wherer "a" is constant aand "x" is variable. a is called the base of the function and it should be grater then 0 (zero).

example of exponantial function : 

`e^x`, `a^x`, `2^x`

standard format of logarithm

formula:-

`a^x` = y ⇄ x = `\log_ay`

how to calculate sum

type:-1 convert simple forme to logrithmic forme

question 1) `A^x` = y

step 1: 

write formula
`a^x` = y ⇄ x = `\log_ay`
step 2:  

question and formula compare, in question given left side term `a^x`= y
step 3: 

write right side term x = `\log_ay`
step:-4

put value in step 3 frome step 2

type:-1 convert logarithm forme to simple forme

question 1) x = `\log_ay`

step 1: 

write formula
`a^x` = y ⇄ x = `\log_ay`
step 2:  

question and formula compare, in question given right side term x = `\log_ay`
step 3: 

write left side term `a^x` = y
step:-4

put value in step 3 frome step 2

question: `2^3` = 8 convert to logaritm forme

step 1: 
write formula
`a^x` = y ⇄ x = `\log_ay`
step 2: 
question and formula compare, in question given left side term `A^x` = y,a=2,x=3, y=8
step 3: 
write right side term x = `\log_ay`,
step 4: 
put value in step 3 frome step 2 (a=2, x=3, y=8)
answer : 

x = `\log_ay`
3 = `\log_28` or `\log_28` = 3

extra sum

1) `log_7`(49)
Answer:- 2
2) `log_2`(`\frac{1}{8}`)
Answer:- -3
3) `log_5`(625)
Answer:- 4

addition formula in logarithm

addition formula:-

`\log_ax` + `\log_ay` ⇄ `\log_axy`
explain

if base(means value of a in formula) are same and logaritm term are in addition pattern.multiplied all addition term with each other. it means 2 + 3 + 4 = 2 `*`3 `*`4
note: 

if base are same then applied this formula otherwise not.

how to calculate sum

1) `\log_ax` + `\log_ay`

step 1: 
write formula
`\log_ax` + `\log_ay` ⇄ `\log_axy`

step 2: 
question comper with formula, in question given left side term `\log_ax` + `\log_ay`

step 3: 
we know that the explaination of two term in addition then the multiplication is given solution in logarithm

step 4: 
answer is = `\log_axy`

Question : `log_23 + log_25`

step 1: 
write formula
`\log_ax` + `\log_ay` ⇄ `\log_axy`

step 2: 
question comper with formula, in question given left side term `\log_ax` + `\log_ay`

step 3: 
write right side term x = `log_ay`,

step 4:
put value in step 3 frome step 2 (a= 2, x=3, y=5)

answer: 

x = `log_2``3*5`
 =`log_15`

subtraction formula in logarithm

subtraction formula:-

`\log_ax` - `\log_ay` ⇄ `\log_a(fracx\y)`
explainif base(means value of "a" in formula) are same and logaritm term are in subtraction pattern.multiplied all addition term with each other. it means 2 `-` 3 = 2 `/`3
note: if base are same then applied this formula otherwise not.
how to calculate sum

1) `\log_ax - \log_ay`

step 1: 
write formula `\log_ax - \log_ay` ⇄ `\log_a(fracx\y)`

step 2: 
question comper with formula, in question given left side term `\log_ax - \log_ay`

step 3: 
we know that the explaination of two term in addition then the dividon is given solution in logarithm

step 4: 
answer is = `\log_a(fracx\y)`

Question : `log_23 - log_25`

step 1: 
write formula
`\log_ax - \log_ay` ⇄ `\log_a(fracx\y)`

step 2: 
question comper with formula, in question given left side term `\log_ax - \log_ay`(x=3, y=5,a=2)

step 3: 
write right side term x = `log_a(fracx\y)`,

step 4:
put value in step 3 frome step 2(x=3, y=5,a=2)

answer: 
x = `log_a(frac3\5)`
 =`log_a(\frac3\5)`

extra sum

1) `log_3` (84) - `log_3`(28) - `_3log_3 1`
Answer:- 0
2) Prove that - `\frac{1}{log_a (abc)}` + `\frac{1}{log_b (abc)}` + `\frac{1}{log_c (abc)}` = 1
Answer:- 1
3) Prove that - `\frac{1}{log_xy (xyz)}` + `\frac{1}{log_yz (xyz)}` + `\frac{1}{log_zx (xyz)}` = 2
Answer:- 2

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