# 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

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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 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 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.

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