[MAI 2.11-2.12] EXPONENTS AND LOGARITHMS-II-neha
Question
[try to solve without GDC]
Write down the following values
▶️Answer/Explanation
Ans
Question
[try to solve without GDC]
Find the value of \(x\) in the following equations
(a) (i) \(\log_{2}x = 3\) (ii) \(\log_{x}8 = 3\)
(b) (i) \(\log_{5}x = 2\) (ii) \(\log_{x}25 = 2\)
(c) (i) \(\log_{4}2x = 2\) (ii) \(\log_{2x}16 = 2\)
(d) (i) \(\log x = 2\) (ii) \(\ln x = 4\)
▶️Answer/Explanation
Ans
(a) (i) \(x = 8\) (ii) \(x = 2\)
(b) (i) \(x = 25\) (ii) \(x = 5\)
(c) (i) \( 2x =16 \Leftrightarrow x = 8\) (ii) \(4x^{2} = 16 \Leftrightarrow x = 2\)
(d) (i) \(x = 100\) (ii) \(e^{4}\)
Question
Find the following values in terms of \(k\)
▶️Answer/Explanation
Ans
Question
[try to solve without GDC]
Solve the following equations
(a) \(\log _{3}(x+1)=2\)
(b) \(\log (x+1)=2\)
(c) \(\ln (x+1)=2\)
▶️Answer/Explanation
Ans
(a) \(x = 8\) (b) \(x = 99\) (c) \(e^{2}-1\)
Question
[try to solve without GDC]
Solve the following equations
(a) (i) \(\log _{7}(x+5)=0\) (ii) \(\log _{7}(x+5)=0\)
(a) (i) \(\log (x+5)=0\) (ii) \(\log (x+5)=0\)
(a) (i) \(\ln (x+5)=0\) (ii) \(\ln (x+5)=0\)
▶️Answer/Explanation
Ans
(a) (i) \(x + 5 = 1 \Leftrightarrow x = -4\) (ii) \(x + 5 = 7 \Leftrightarrow x = 2\)
(b) (i) \(x + 5 = 1 \Leftrightarrow x = -4\) (ii) \(x + 5 = 10 \Leftrightarrow x = 5\)
(c) (i) \(x + 5 = 1 \Leftrightarrow x = -4\) (ii) \(x + 5 = e \Leftrightarrow x = e – 5\)