Sasi Math (Revised for 1024)

Scroll:Logarithms >> Find the value and solve the equation >> saq (4208)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

Find the value of following

log₆6⁵

Answer:_______________

Simplify the following.

5log₁₀2 + 2log₁₀3 - 6log₆₄4

log₁₀

Answer:_______________

Solve the following equation. (use / )

x + 2log₂₇9 = 0

Answer:_______________

Simplify the following.

log₂₅35 - log₂₅10

(A) log₂₅7 /2 (B) log₂₄7/ 2 (C) log₂₅9/ 2 (D) log₂₄6 /7

1) B
2) D
3) A
4) C

Answer:_______________

Find the value of following

log₃ $\frac{(1}{81)}$

Answer:_______________

Find the value of following

Let log₁₀ 0.0001 = x

Answer:_______________

Solve the following equation.

log_x0.001 = -3

Answer:_______________

Simplify the following.

log₁₀3 + log₁₀3

(A) log₁₀8 (B) log₁₀7 (C) log₁₀9 (D) log₁₀6

1) D
2) A
3) B
4) C

Answer:_______________

Find the value of following

log₇343

Answer:_______________

10)

Find the value of following

log_{$\frac{(1}{2)}$}8 = x

Answer:_______________

Find the value of following

log₆6⁵

Answer: 5

SOLUTION 1 :

log₆6⁵= 5

Simplify the following.

5log₁₀2 + 2log₁₀3 - 6log₆₄4

log₁₀ Answer: $\frac{72}{25}$

SOLUTION 1 :

5log₁₀2 + 2log₁₀3 - 6log₆₄4

= 5log₁₀2⁵ + log₁₀3² - log₆₄4⁶

= log₁₀32 + log₁₀9 - log₆₄64x64

= log₁₀32x9 - 2log₆₄64

= log₁₀288 - 2log₁₀10

= log₁₀ $\frac{288}{100}$

= log₁₀ $\frac{72}{25}$

Solve the following equation. (use / )

x + 2log₂₇9 = 0

Answer: $\frac{-4}{3}$

SOLUTION 1 :

x + 2log₂₇9 = 0

x = - 2log₂₇9

⇒ 27^x = 9^-2

(3³)^x = (3²)^-2 [ Change the base into 3 ]

⇒ 3^3x = 3^-4 [ Change the base into 3 ]

⇒ x = $\frac{-4}{3}$

Simplify the following.

log₂₅35 - log₂₅10

(A) log₂₅7 /2 (B) log₂₄7/ 2 (C) log₂₅9/ 2 (D) log₂₄6 /7

1) A
2) D
3) C
4) B

Answer: 1

SOLUTION 1 :

log₂₅35 - log₂₅10

= log₂₅( $\frac{35}{10)}$

= log₂₅7/ 2

Find the value of following

log₃ $\frac{(1}{81)}$

Answer: -4

SOLUTION 1 :

log₃ $\frac{(1}{81)}$ = log3 $\frac{(1}{3}$ ₄)

= log₃1 - log₃3⁴

= 0= 4log₃3 = 0 - 4 = -4

Find the value of following

Let log₁₀ 0.0001 = x

Answer: -4

SOLUTION 1 :

log₁₀ 0.0001 = x

= 10^x = 0.0001 = 10^-4

= x = -4

Solve the following equation.

log_x0.001 = -3

Answer: 10

SOLUTION 1 :

logx0.001 = -3

= x^-3 = 0.001 = 10^-3

x = 10.

Simplify the following.

log₁₀3 + log₁₀3

(A) log₁₀8 (B) log₁₀7 (C) log₁₀9 (D) log₁₀6

1) B
2) D
3) C
4) A

Answer: 3

SOLUTION 1 :

log₁₀3 + log₁₀3

= 2log₁₀3 = log₁₀3²

= log₁₀9

Find the value of following

log₇343

Answer: 3

SOLUTION 1 :

log₇343

= log₇7 = 3log₇7

= 3(1) = 3

10)

Find the value of following

log_{$\frac{(1}{2)}$}8 = x

Answer: -3

SOLUTION 1 :

log_{$\frac{(1}{2)}$}8 = x

⇒ ( $\frac{1}{2)}$ ^x = 8 = 2³

= 2^-x = 2³ or x = -3