HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Book Answers

 AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Book Answers

Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Books Solutions

 Board AP Board Materials Textbook Solutions/Guide Format DOC/PDF Class 10th Subject Maths Chapters Maths Chapter 1 Real Numbers Ex 1.5 Provider Hsslive

2. Click on the Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Answers.
3. Look for your Andhra Pradesh Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks PDF.
4. Now download or read the Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions for PDF Free.

AP Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

Question 1.
Determine the values of the following,
i) log255

ii) log813

iii) log2(116)

iv) log71
log71 = log770 = 0 log77 = 0

v) logx√x

vi) log2512
log2512 = log229 [∵ 512 = 29]
= 9log22 [∵ log xm = m log x]
= 9 × 1 [∵ logaa = 1]
= 9

vii) log100.01

viii) log23(827)

ix) 22+log23
22+log23 = 22 . 2log23 [∵ am . an = am+n]
= 4 × 3 [∵ logaN = N]
= 12

Question 2.
Write the following expressions as log N and find their values.

i) log 2 + log 5
log 2 + log 5
= log 2 × 5 [∵ log m + log n = log mn]
= log 10
= 1

ii) log2 16 – log2 2

iii) 3 log644

iv) 2 log 3 – 3 log 2
2 log 3 – 3 log 2
= log 32 – log 23
= log 9 – log 8
= log 98

v) log 10 + 2 log 3 – log 2
log 10 + 2 log 3 – log 2
= log 10 + log 32 – log 2
= log 10 + log 9 – log 2 [∵ m log a = log am]
= log 10×92 [∵ log a + log b = log ab; log a – log b = log 𝑎𝑏]
= log 45

Question 3.
Evaluate each of the following in terms of x and y, if it is given x = log23 and y = log2 5.

i) log215
log215 = log2 3 × 5
= log23 + log25 [∵ log mn = log m + log n]
= x + y

ii) log27.5

iii) log260
log260 = log222 × 3 × 5
= log222 + log23 + log25
= 2 log22 + x + y
= 2 + x + y

iv) log26750

log26750
= log22 × 33 × 53
= log22 + log233 + log253
= 1 + 3 log23 + 3 log25
= 1 + 3x + 3y

Question 4.
Expand the following,
i) log 1000
log 1000 = log 103
= 3 log 10
= 3 × 1
= 3

ii) log[128625]

iii) log x2y3z4
log x2y3z4 = logx2 + logy3 + logz4 [∵ log ab = log a + log b]
= 2 log x + 3 log y + 4 log z
[∵ log am = m log a]

iv) log𝐩2𝐪3𝐫

iv) log𝑥3𝑦2‾‾‾√

Question 5.
If x2 + y2 = 25xy, then prove that 2 log (x + y) = 3log3 + logx + logy.
Given: x2 + y2 = 25xy
We know that (x + y)2 = x2 + y2 + 2xy
= 25xy + 2xy [∵ x2 + y2 = 25xy given]
(x + y)2 = 27xy
Taking ‘log’ on both sides
log (x + y)2 = log 27xy
2 log (x + y) = log 27 + log x + log y
= log 33 + log x + log y
⇒ 2 log (x + y) = 3log3 + log x + log y

Question 6.
If log(𝐱+𝐲3) = 12 (log x + log y), then find the value of 𝑥𝑦+𝑦𝑥.

(squaring on both sides)
⇒ (x + y)2 = (3√xy)2
⇒ x2 + y2 + 2xy = 9xy
⇒ x2 + y2 = 9xy – 2xy = 7xy

Question 7.
If (2.3)x = (0.23)y = 1000 then find the value of 1𝑥−1𝑦.
Given (2.3)x = (0.23)y = 1000 = 103

Question 8.
If 2x+1 = 31-x then find the value of x.
Given: 2x+1 = 31-x
log 2x+1 = log 31-x
(x + 1) log 2 = (1 – x) log 3
x log 2 + log 2 = log 3 – x log 3
x log 2 + x log 3 = log 3 – log 2
x (log 3 + log 2) = log 3 – log 2

Question 9.
Is
Let log102 = x
Then 10x = 2
But 2 can’t be written as 10x for any value of x
∴ log 2 is irrational.

Let log10100 = x
⇒ log10102 = x
⇒ 2 log1010 = x = 2
∴ log 100 is rational.
∴ log 100 = 2
Hence rational.

Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks for Exam Preparations

Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 exam preparation. The AP Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Books State Board syllabus with maximum efficiency.

FAQs Regarding Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions

Can we get a Andhra Pradesh State Board Book PDF for all Classes?

Yes you can get Andhra Pradesh Board Text Book PDF for all classes using the links provided in the above article.

Important Terms

Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5, AP Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks, Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5, Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbook solutions, AP Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks Solutions, Andhra Pradesh Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5, AP Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks, Andhra Pradesh State Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5, Andhra Pradesh State Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbook solutions, AP Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks Solutions,
Share: