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August 2, 2023
Go through the entire page to know How To Solve Logarithm Questions Quickly. You will get to know easy tricks and formulas of Logarithms problems.
Question 1 If log 27= 1.431, then the value of log 9 is?
Option:
A) 0.945
B) 0.934
C) 0.958
D) 0.954
Solution: log 27= 1.431
\implies log(3)3= 1.431
\implies 3log 3= 1.431
\implies log3= 0.477
therefore, log9= log 32= 2 log3= (2×0.477)= 0.954
Correct Answer: D
Question 2 If log \frac{a}{b} \ +log \frac{b}{a} \ = log(a+b), then
A) a-b=1
B) a=b
C) a+b=1
D)a2-b2 = 1
Solution: log \frac{a}{b} \ + log \frac{b}{a} \ = log(a+b)
\implies log (a+b)= log ( \frac{a}{b} \ x \frac{b}{a}) \ = log 1
so, a+b=1
Correct Answer: C
Question: Solve the equation log x= 1- log(x-3)
A) 2
B) \frac{1}{2} \
C) 5
D) 4
Solution: By combining both the equation we get
logx + log (x-3)=1
log(x(x-3))= log 101
Now convert it into exponential form,
x (x-3)= 101
x2 – 3x-10= 0(x-5) (x+2)=0x= -2, x=5
By solving this equation we get two values for x.x= -2, x=5
Put the different value of x in different equation and solve them,x= -2log(-2) = 1- log (-2-3)
x= 5log5 = 1-log(5-3)log5 = 1-log2
Negative value is not considered in logarithm. So, we have a single value of x i.e, x=5.
Correct Answer : C.
Question 4 log9 (3log2 (1+log3 (1+2log2 x)))= \frac{1}{2} \ . Find x.
C) 1
Solution : log9 (3log2 (1+log3 (1+2log2 x)))= \frac{1}{2} \ .
3log2 (1+log3 (1+2log2 x))= 9^{\frac{1}{2}} = 3
log2(1+log3(1+2log2 x) = 1
1+log3 (1+2log2 x)=2^1
log3 (1+2log2 x)=2^1 -1
log3 (1+2log2 x) = 1
(1+2log2 x) = 3^1
1+ 2log2 x= 3
2log2 x = 2
log2x = 1
x= 2
Correct Answer: A
Question 5 If log 10 5+ log(5x+1) = log 10 (x+5) +1, Find the value of X?
Option
A) 3
B) 1
C) 10
D) 5
Solution : log 10 5+ log(5x+1) = log 10 (x+5) +1.
log 10 5+ log(5x+1) = log 10 (x+5) +log 10 10
log10 [5 (5x+1) ] = log10( 10 (x+5)]
5 (5x+1) = 10 (x+5)
5x+1 = 2x+ 10
3x= 9
x=3.
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