4.3.5 Logarithms to general base

➤➤

120 130

➤

A.Findxif

(i) 8=log 2 x (ii) 3=log 2 x (iii) 4=lnx

(iv) 6=log 3 x (v) 4=log 3 x (vi) 2=lnx

B.Evaluate

(i) lne^3 (ii) log 4 ( 256 ) (iii) log 327

(iv) log 981 (v) log 4 2(vi)ln(e^2 )^2

(vii) lne^7 (viii) log 3 ( 243 )

4.3.6 Manipulation of logarithms

➤➤

120 131

➤

A.Simplify as a single log

(i) 2 lne^4 +3lne^3 (ii) 3 log 2 x+log 2 x^2

(iii) logax+loga( 2 y) (iv) ln( 3 x)−^12 ln( 9 x^2 )

(v) 2 logax+3lnx (vi) logax−log 2 ax (vii) lnx+2logax^2

B. Expand each as a linear combination of numbers and logs in simplest form

(i) ln( 3 x^2 y) (ii) log 2 ( 8 x^2 y^3 ) (iii) ln(eA/eB)

(iv) loga(axya) (v) log 2 a( 8 a^3 x^2 y^4 ) (vi) ln(x^2 y^2 z^2 )

C.Simplify

(i)

aloga^6 x^2 ln(e^3 x)

2 axlog 2 ( 4 x)

(ii)

a(x−^1 )

2

a^2 xa^3

(ax)^2 ax^2 ln(e^2 a)

D.Evaluate

(i) log 232 (ii) log 10100 (iii) log 749

(iv) log 5625 (v) logaa

1

(^2) (vi) lne^2001
(vii) log 1 / 864 (viii) ln
1
e
(ix) log 82
E. Simplify(logtoanybase)
(i)
log 81
log 9
(ii)
log 8
log 2
(iii)
log 49
log 343
(iv) 5 log 2−3 log 32 (v)^12 log 49
F.Given that
ln
1
y

1
2
ln(x+ 1 )−
1
2
ln(x− 1 )+ 3 x+lnx+C
whereCis an arbitrary constant, obtain an explicit expression foryin terms ofx.