Question

Write each of the following expressions as log N. Determine the value of N. (You can assume the base is 10, but the results are identical which ever base is used).(i) log 2 + log 5 (ii) log 16 - log 2 (iii) 3 log 4(iv) 2 log 3 - 3 log 2 (v) log243 + log1 (vi) log 10 + 2 log 3 - log 2

Answer 1

(i) log 2 + log 5

$logm+logn=log(m*n)=logN$

$log2+log5=log(2*5)=logN$=log10

So, N=10

(ii) log 16 - log 2

$logm-logn=log(m/n)=logN$

$log16-log2=log(16/2)=logN$=log8

Hence, N =8

(iii) 3 log 4

$xlogy=logy^{x}$

$3log4=log4^{3}$=log64=logN

N =64

(iv) 2 log 3 - 3 log 2

$2log3=log3^{2}$=log9

$3log2=log2^{3}$=log8

log9-log8=log(9/8)=log(1.125)

N=1.125

(v) log243 + log1

log1=0

So,log243 + log1 =log243=logN

N=243

(vi) log 10 + 2 log 3 - log 2

   $2log3=log3^{2}$=log9

log9-log2=log(9/2)=log4.5

log4.5+log10=log45=logN

N=45.

Answer 2

Answer:

(I)a n=10

(ii)a n=8

(iii)a n=64

(iv)a n=1.125

(v)a n=243

(vi)a n=45