Maths Logarithms Exercise9-1
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Q1 Convert the following to logarithmic form:
(i) 52 = 25
(ii) a5 =64
(iii) 7x =100
(iv) 9° = 1
(v) 61 = 6
(vi) 3-2 = 19
(vii) 10-2 = 0.01
(viii) (81)3/4 = 27
Q2 Convert the following into exponential form:
(i) log2 32 = 5
(ii) log3 81=4
(iii) log31/3= -1
(iv) log3 4= 2/3
(v) log8 32= 5/3
(vi) log10 (0.001) = -3
(Vii) log2 0.25 = -2
(viii) loga (1/a) =-1
Q3 By converting to exponential form, find the values of:
(i) log2 16
(ii) log5 125
(iii) log4 8
(iv) log9 27
(v) log10(.01)
(vi) log7 1/7
(vii) log5 256
(Viii) log2 0.25
Q4 Solve the following for x :
Q5 Given log10a = b, express 10b2b-3 in terms of a.
Q6 Given log10 x= a, log10 y = b and log10 z =c,
(i) write down 102a-3 in terms of x.
(ii) write down 103b-1 in terms of y.
(iii) if log10 P = 2a + b/2– 3c, express P in terms of x, y and z.
Q7 If log10x = a and log10y = b, find the value of xy.
Q8 Given log10 a = m and log10 b = n, express a3/b2 in terms of m and n.
Q9 Given log10a= 2a and log10y = –b2
(i) write 10a in terms of x.
(ii) write 102b+1 in terms of y.
(iii) if log10P= 3a -2b, express P in terms of x and y
Q10 If log2 y = x and log3 z = x, find x in terms of y and z.
Q11 If log2 x = a and log5y = a, write 1002a-1 in terms of x and y.
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