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

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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 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks Solutions and answers for students are now available in pdf format. Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Book answers and solutions are one of the most important study materials for any student. The Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 books are published by the Andhra Pradesh Board Publishers. These Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 textbooks are prepared by a group of expert faculty members. Students can download these AP Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 book solutions pdf online from this page.

Andhra Pradesh Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks Solutions PDF

Andhra Pradesh State Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Books Solutions with Answers are prepared and published by the Andhra Pradesh Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of AP Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Andhra Pradesh Board STD 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks. These Andhra Pradesh State Board Class 10th Maths Chapter 1 Real Numbers Ex 1.5 Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Andhra Pradesh Board.

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

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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
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 1

ii) log₈₁3
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 2

iii) log₂(116)
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 4

iv) log₇1
Answer:
log₇1 = log₇7⁰ = 0 log₇7 = 0

v) log_x√x
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 5

vi) log₂512
Answer:
log₂512 = log₂2⁹ [∵ 512 = 2⁹]
= 9log₂2 [∵ log x^m = m log x]
= 9 × 1 [∵ log_aa = 1]
= 9

vii) log₁₀0.01
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 6

viii) log23(827)
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 7

ix) 22+log23
Answer:
22+log23 = 2² . 2log23 [∵ a^m . aⁿ = a^m+n]
= 4 × 3 [∵ logaN = N]
= 12

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

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

ii) log₂ 16 – log₂ 2
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 8

iii) 3 log₆₄4
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 9

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

v) log 10 + 2 log 3 – log 2
Answer:
log 10 + 2 log 3 – log 2
= log 10 + log 3² – log 2
= log 10 + log 9 – log 2 [∵ m log a = log a^m]
= 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
Answer:
log₂15 = log₂ 3 × 5
= log₂3 + log₂5 [∵ log mn = log m + log n]
= x + y

ii) log₂7.5
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 10

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

iv) log₂6750
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 11
log₂6750
= log₂2 × 3³ × 5³
= log₂2 + log₂33 + log₂5³
= 1 + 3 log₂3 + 3 log₂5
= 1 + 3x + 3y

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

ii) log[128625]
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 12

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

iv) log𝐩2𝐪3𝐫
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 13

iv) log𝑥3𝑦2‾‾‾√
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 14

Question 5.
If x² + y² = 25xy, then prove that 2 log (x + y) = 3log3 + logx + logy.
Answer:
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.
Answer:
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 15
(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.
Answer:
Given (2.3)^x = (0.23)^y = 1000 = 10³
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 17

Question 8.
If 2^x+1 = 3^1-x then find the value of x.
Answer:
Given: 2^x+1 = 3^1-x
log 2^x+1 = log 3^1-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
AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5 18

Question 9.
Is
i) log 2 is rational or irrational? Justify your answer.
Answer:
Let log₁₀2 = x
Then 10^x = 2
But 2 can’t be written as 10^x for any value of x
∴ log 2 is irrational.

ii) log 100 is rational or irrational? Justify your answer.
Answer:
Let log₁₀100 = x
⇒ log₁₀10² = x
⇒ 2 log₁₀10 = x = 2
∴ log 100 is rational.
∴ log 100 = 2
Hence rational.

AP Board Textbook Solutions PDF for Class 10th Maths

AP Board Class 10 Maths Chapter 1 Real Numbers Textbook Solutions PDF

AP Board Class 10 Maths Chapter 2 Sets Textbook Solutions PDF

AP Board Class 10 Maths Chapter 3 Polynomials Textbook Solutions PDF

AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Textbook Solutions PDF

AP Board Class 10 Maths Chapter 5 Quadratic Equations Textbook Solutions PDF

AP Board Class 10 Maths Chapter 6 Progressions Textbook Solutions PDF

AP Board Class 10 Maths Chapter 7 Coordinate Geometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 8 Similar Triangles Textbook Solutions PDF

AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Textbook Solutions PDF

AP Board Class 10 Maths Chapter 10 Mensuration Textbook Solutions PDF

AP Board Class 10 Maths Chapter 11 Trigonometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Textbook Solutions PDF

AP Board Class 10 Maths Chapter 13 Probability Textbook Solutions PDF

AP Board Class 10 Maths Chapter 14 Statistics Textbook Solutions PDF

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.

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Tuesday, June 7, 2022