Question

simpli each of the following expression as log N 2) 3log 4​

Answer 1

Step by step

i) log 2 + log 5

logm+logn=log(m*n)=logNlogm+logn=log(m∗n)=logN

log2+log5=log(2*5)=logNlog2+log5=log(2∗5)=logN =log10

So, N=10

(ii) log 16 - log 2

logm-logn=log(m/n)=logNlogm−logn=log(m/n)=logN

log16-log2=log(16/2)=logNlog16−log2=log(16/2)=logN =log8

Hence, N =8

(iii) 3 log 4

xlogy=logy^{x}xlogy=logy

x

3log4=log4^{3}3log4=log4

3

=log64=logN

N =64

(iv) 2 log 3 - 3 log 2

2log3=log3^{2}2log3=log3

2

=log9

3log2=log2^{3}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}2log3=log3

2

=log9

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

log4.5+log10=log45=logN

N=45.