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Transcript
7
ACC-MT- LOGARITHM
Practice Problem
Q.1
Q.2
Q.3
Find the logarithms of the following numbers to the base 2:
1
1
(i) 3 8
(ii) 2 2
(iii) 5
(iv) 7
8
2
1
Find the logarithms of the following numbers to the base
3
1
1
(i) 81
(ii) 3 3
(iii) 7
(iv) 9 3
(v) 4
9 3
3
Find all number a for which each of the following equalities hold true?
(i)
(iii)
Q.4
(ii)
(iv)
log10 a (a  3)  = 1
log2(a2 – 5) = 2
Find all values of x for which the following equalities hold true?
(i)
(iv)
Q.5
log2a = 2
log1/3(a2 – 1) = – 1
log 2 x 2 = 1
log1/2(2x + 1) = log1/2(x + 1)


If 2 3  5  13  48  =


(ii)
(v)
log3x = log3(2 – x)
log1/3(x2 + 8) = – 2
(iii)
log 4 x 2 = log4x
b where a and b are natural number find (a + b).
a 
Answer key
Q.1 (i) 1, (ii) 3/2, (iii) – 1/5, (iv) – 3/7
Q.2 (i) – 4, (ii) – 1/3, (iii) 1/7, (iv) – 5/2, (v) 9/4
Q.3 (i) 4, (ii) –5, 2, (iii) –2, 2, (iv) –3, 3
Q.4 (i)
2 ,  2 , (ii) 1, (iii) 1, (iv) 0, (v) 1, – 1
PRINCIPAL PROPERTISE OF LOGARITHM :
(1)
If m, n are arbitrary positive real numbers where
a>0 ; a 1
logam + logan = loga mn
(m > 0, n > 0)
Proof : Let
x1 = logam
;
m = ax
Now
x2 = loga n
mn = ax ; a x 2
n = a x2
;
mn = a x1  x 2
x1 + x2 = logamn
logam + logan = logamn
(2)
log a
m
= logam – logan
n
m
x x
=a 1 2
n
x1 – x2 = log a
m
n
logam – logan = log a
m
n
BANSAL CLASSES Private Ltd. ‘Gaurav Tower’, A-10, Road No.-1, I.P.I.A., Kota-05
Q.5 8