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August 3, 2023
Logarithm is the way to represent exponential expression as shown in the example .
Example : a x = y is a exponential expression And it can also be written as x = log a y . which is a logarithm expression.
Question: log 100 = 2Taking LHS
log 102
= 2 log 10
= 2 × 1 (∴ Log 10 = 1 )
= 2 .
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Question 1 Which of the following statement is not correct?
Option
A) log (1 + 2 + 3) = log 1 + log 2 + log 3
B) log( 2+3) = log (2×3)
C) log10 1 = 0
D) log10 10 = 1
Solution:
a) log( 1+2+3) = log6 = log (1×2×3) = log1+ log2+log3
b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3
log (2 + 3) ≠ log (2 x 3)
c) Since, loga 1=0,so log10 1=0
d) Since, loga a = 1so, log10 10 = 1.
Correct Answer : B
Question 2 If X is an integer then solve(log2 X)2– log2x4-32 = 0
Solution : Let us consider,(log2 X)2– log2x4-32 = 0 —— equation 1
let log2 x= y
equation 1 = y2– 4y-32=0
y2-8y+ 4y – 32= 0
y(y-8) + 4(y-8) =0
(y-8) (y+4)= 0
y=8, y= -4
log2X=8 or, log2X = -4
X= 28 = 256, 0r 2-4 = \frac{1}{16} \
Since, X is an integer so X = 256.
Question 3 Solve for x: \log_{2}(x + 3) + log_{2}(x – 1) = 3
Solution: Combine the logarithms using the logarithm property log(a) + log(b) = log(a * b):\log_{2}((x+3)\times(x-1)) = 3
(x+4)(x-2)=0
x = -4,2
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