StudentAidUnit 2: Logarithms — Exercise 2 2
9th Class Mathematics · Unit 2: Logarithms
2.2.1.Express each of the following in logarithmic form: (i) 10^3=1000 (ii) 2^8=256 (iii) 3^-3=1/27 (iv) 20^2=400 (v) 16^(-1/4)=1/2 (vi) 11^2=121 (vii) p=q^r (viii) (32)^(-1/5)=1/2
Formula
logb(x)=y Leftrightarrow by=x ; b>0, x>0, bneq1
Result
(i)
log101000=3
(ii)
log2 256=8
(iii)
log3127=-3
(iv)
log20400=2
(v)
log1612=-14
(vi)
log11121=2
(vii)
logq p=r
(viii)
log3212=-15
2.2.2.Express each of the following in exponential form: (i) log5 125=3 (ii) log2 16=4 (iii) log23 1=0 (iv) log5 5=1 (v) log2(1/8)=-3 (vi) 1/2=log9 3 (vii) 5=log10 100000 (viii) log4(1/16)=-2
Formula
logb(x)=y Leftrightarrow by=x ; b>0, x>0, bneq1
Result
(i)
53=125
(ii)
24=16
(iii)
230=1
(iv)
51=5
(v)
2-3=18
(vi)
9^{12=3
(vii)
105=100000
(viii)
4-2=116
2.2.3.Find the value of x in each of the following: (i) log_x 64=3 (ii) log_5 1=x (iii) log_x 8=1 (iv) log_10 x=-3 (v) log_4 x=3/2 (vi) log_2 1024=x
Working
(i)
logx 64=3 ⇒ x3=64 ⇒ x3=43
Result
(i)
x=4
Working
(ii)
log5 1=x ⇒ 5x=1 ⇒ 5x=50
Result
(ii)
x=0
Working
(iii)
logx 8=1 ⇒ x1=8
Result
(iii)
x=8
Working
(iv)
log10x=-3 ⇒ 10-3=x=1103
Result
(iv)
x=11000
Working
(v)
log4 x=32 ⇒ 4^{32=x=(22)^{32=23
Result
(v)
x=8
Working
(vi)
log2 1024=x ⇒ 2x=1024=210
Result
(vi)
x=10