{"id":5170,"date":"2021-03-04T11:52:35","date_gmt":"2021-03-04T06:22:35","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=5170"},"modified":"2021-09-15T11:39:30","modified_gmt":"2021-09-15T06:09:30","slug":"ap-ssc-10th-class-maths-solutions-chapter-1-ex-1-5","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-ssc-10th-class-maths-solutions-chapter-1-ex-1-5\/","title":{"rendered":"AP SSC 10th Class Maths Solutions Chapter 1 Real Numbers Ex 1.5"},"content":{"rendered":"

AP State Board Syllabus\u00a0AP SSC 10th Class Maths Textbook Solutions<\/a> Chapter 1 Real Numbers Ex 1.5 Textbook Questions and Answers.<\/p>\n

AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.5<\/h2>\n

10th Class Maths 1st Lesson Real Numbers Ex 1.5 Textbook Questions and Answers<\/h3>\n

Question 1.
\nDetermine the values of the following,
\ni) log25<\/sub>5
\nAnswer:
\n\"AP<\/p>\n

\"AP<\/p>\n

ii) log81<\/sub>3
\nAnswer:
\n\"AP
\n\"AP<\/p>\n

iii) log2<\/sub>(\\(\\frac{1}{16}\\))
\nAnswer:
\n\"AP<\/p>\n

iv) log7<\/sub>1
\nAnswer:
\nlog7<\/sub>1 = log7<\/sub>70<\/sup> = 0 log7<\/sub>7 = 0<\/p>\n

\"AP<\/p>\n

v) logx<\/sub>\u221ax
\nAnswer:
\n\"AP<\/p>\n

vi) log2<\/sub>512
\nAnswer:
\nlog2<\/sub>512 = log2<\/sub>29<\/sup>\u00a0 \u00a0 [\u2235 512 = 29<\/sup>]
\n= 9log2<\/sub>2\u00a0 \u00a0[\u2235 log xm<\/sup> = m log x]
\n= 9 \u00d7 1\u00a0 \u00a0 [\u2235 loga<\/sub>a = 1]
\n= 9<\/p>\n

vii) log10<\/sub>0.01
\nAnswer:
\n\"AP<\/p>\n

viii) \\(\\log _{\\frac{2}{3}}\\left(\\frac{8}{27}\\right)\\)
\nAnswer:
\n\"AP<\/p>\n

ix) \\(2^{2+\\log _{2} 3}\\)
\nAnswer:
\n\\(2^{2+\\log _{2} 3}\\) = 22<\/sup> . \\(2^{\\log _{2} 3}\\)\u00a0 \u00a0[\u2235 am<\/sup> . an<\/sup> = am+n<\/sup>]
\n= 4 \u00d7 3 [\u2235 \\(\\log _{\\mathrm{a}} \\mathrm{N}\\) = N]
\n= 12<\/p>\n

\"AP<\/p>\n

Question 2.
\nWrite the following expressions as log N and find their values.
\ni) log 2 + log 5
\nAnswer:
\nlog 2 + log 5
\n= log 2 \u00d7 5\u00a0 \u00a0[\u2235 log m + log n = log mn]
\n= log 10
\n= 1<\/p>\n

ii) log2<\/sub> 16 – log2<\/sub> 2
\nAnswer:
\n\"AP<\/p>\n

iii) 3 log64<\/sub>4
\nAnswer:
\n\"AP<\/p>\n

iv) 2 log 3 – 3 log 2
\nAnswer:
\n2 log 3 – 3 log 2
\n= log 32<\/sup> – log 23<\/sup>
\n= log 9 – log 8
\n= log \\(\\frac{9}{8}\\)<\/p>\n

v) log 10 + 2 log 3 – log 2
\nAnswer:
\nlog 10 + 2 log 3 – log 2
\n= log 10 + log 32<\/sup> – log 2
\n= log 10 + log 9 – log 2\u00a0 \u00a0 [\u2235 m log a = log am<\/sup>]
\n= log \\(\\frac{10 \\times 9}{2}\\)\u00a0 \u00a0 [\u2235 log a + log b = log ab; log a – log b = log \\(\\frac{a}{b}\\)]
\n= log 45<\/p>\n

\"AP<\/p>\n

Question 3.
\nEvaluate each of the following in terms of x and y, if it is given x = log2<\/sub>3 and y = log2<\/sub> 5.
\ni) log2<\/sub>15
\nAnswer:
\nlog2<\/sub>15 = log2<\/sub> 3 \u00d7 5
\n= log2<\/sub>3 + log2<\/sub>5\u00a0 \u00a0[\u2235 log mn = log m + log n]
\n= x + y<\/p>\n

ii) log2<\/sub>7.5
\nAnswer:
\n\"AP<\/p>\n

iii) log2<\/sub>60
\nAnswer:
\nlog2<\/sub>60 = log2<\/sub>22<\/sup> \u00d7 3 \u00d7 5
\n= log2<\/sub>22<\/sup> + log2<\/sub>3 + log2<\/sub>5
\n= 2 log2<\/sub>2 + x + y
\n= 2 + x + y<\/p>\n

iv) log2<\/sub>6750
\nAnswer:
\n\"AP
\nlog2<\/sub>6750
\n= log2<\/sub>2 \u00d7 33<\/sup> \u00d7 53<\/sup>
\n= log2<\/sub>2 + log2<\/sub>33 + log2<\/sub>53<\/sup>
\n= 1 + 3 log2<\/sub>3 + 3 log2<\/sub>5
\n= 1 + 3x + 3y<\/p>\n

\"AP<\/p>\n

Question 4.
\nExpand the following,
\ni) log 1000
\nAnswer:
\nlog 1000 = log 103<\/sup>
\n= 3 log 10
\n= 3 \u00d7 1
\n= 3<\/p>\n

ii) \\(\\log \\left[\\frac{128}{625}\\right]\\)
\nAnswer:
\n\"AP<\/p>\n

iii) log x2<\/sup>y3<\/sup>z4<\/sup>
\nAnswer:
\nlog x2<\/sup>y3<\/sup>z4<\/sup> = logx2<\/sup> + logy3<\/sup> + logz4<\/sup> [\u2235 log ab = log a + log b]
\n= 2 log x + 3 log y + 4 log z
\n[\u2235 log am<\/sup> = m log a]<\/p>\n

iv) \\(\\log \\frac{\\mathbf{p}^{2} \\mathbf{q}^{3}}{\\mathbf{r}}\\)
\nAnswer:
\n\"AP<\/p>\n

iv) \\(\\log \\sqrt{\\frac{x^{3}}{y^{2}}}\\)
\nAnswer:
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 5.
\nIf x2<\/sup> + y2<\/sup> = 25xy, then prove that 2 log (x + y) = 3log3 + logx + logy.
\nAnswer:
\nGiven: x2<\/sup> + y2<\/sup> = 25xy
\nWe know that (x + y)2<\/sup> = x2<\/sup> + y2<\/sup> + 2xy
\n= 25xy + 2xy\u00a0 \u00a0 [\u2235 x2<\/sup> + y2<\/sup> = 25xy given]
\n(x + y)2<\/sup> = 27xy
\nTaking ‘log’ on both sides
\nlog (x + y)2<\/sup> = log 27xy
\n2 log (x + y) = log 27 + log x + log y
\n= log 33<\/sup> + log x + log y
\n\u21d2 2 log (x + y) = 3log3 + log x + log y<\/p>\n

Question 6.
\nIf \\(\\log \\left(\\frac{\\mathbf{x}+\\mathbf{y}}{3}\\right)\\) = \\(\\frac{1}{2}\\) (log x + log y), then find the value of \\(\\frac{x}{y}+\\frac{y}{x}\\).
\nAnswer:
\n\"AP
\n(squaring on both sides)
\n\u21d2 (x + y)2<\/sup> = (3\u221axy)2<\/sup>
\n\u21d2 x2<\/sup> + y2<\/sup> + 2xy = 9xy
\n\u21d2 x2<\/sup> + y2<\/sup> = 9xy – 2xy = 7xy
\n\"AP<\/p>\n

Question 7.
\nIf (2.3)x<\/sup> = (0.23)y<\/sup> = 1000 then find the value of \\(\\frac{1}{x}-\\frac{1}{y}\\).
\nAnswer:
\nGiven (2.3)x<\/sup> = (0.23)y<\/sup> = 1000 = 103<\/sup>
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 8.
\nIf 2x+1<\/sup> = 31-x<\/sup> then find the value of x.
\nAnswer:
\nGiven: 2x+1<\/sup> = 31-x<\/sup>
\nlog 2x+1<\/sup> = log 31-x<\/sup>
\n(x + 1) log 2 = (1 – x) log 3
\nx log 2 + log 2 = log 3 – x log 3
\nx log 2 + x log 3 = log 3 – log 2
\nx (log 3 + log 2) = log 3 – log 2
\n\"AP<\/p>\n

Question 9.
\nIs
\ni) log 2 is rational or irrational? Justify your answer.
\nAnswer:
\nLet log10<\/sub>2 = x
\nThen 10x<\/sup> = 2
\nBut 2 can’t be written as 10x<\/sup> for any value of x
\n\u2234 log 2 is irrational.<\/p>\n

ii) log 100 is rational or irrational? Justify your answer.
\nAnswer:
\nLet log10<\/sub>100 = x
\n\u21d2 log10<\/sub>102<\/sup> = x
\n\u21d2 2 log10<\/sub>10 = x = 2
\n\u2234 log 100 is rational.
\n\u2234 log 100 = 2
\nHence rational.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Board Syllabus\u00a0AP SSC 10th Class Maths Textbook Solutions Chapter 1 Real Numbers Ex 1.5 Textbook Questions and Answers. AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.5 10th Class Maths 1st Lesson Real Numbers Ex 1.5 Textbook Questions and Answers Question 1. Determine the values of the following, …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/5170"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=5170"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/5170\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=5170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=5170"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=5170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}