Pls help: 2 Evaluate the following i log 10+103 - Maths - Indices and Logarithms

Question

Pls help:

2 Evaluate the following
i   log   10 + 10 3          
                 
                 
            ii   2 + 1 2  
log   10 - 3 iii   2   log 5   +   log
  8   - 1 2   log 4 iv   2   log   10
3 +   3   log   10 - 2 - 1 3   log   5 - 3
+ 1 2   log   4

Shruti Tyagi · Accepted Answer

Dear student,

ii) 2+12log10-3using logmn=nlogm=2+-32log10=2+-32×1          --[as value of log 10=1]=2-32=4-32=12(iv) 2log103+3log10-2-13log5-3+12log4=2log103+3log10-2-13log5-3+12log22using logmn=nlogm=2×3log10+3×-2log10-13×-3log5+12×2log2=6log10-6log10+log5+log2⏟=6log10-6log10+log5×2     --[using logm+logn=log(m×n)]=6log10-6log10+log10As value of log 10=1=6-6+1=1
Regards

Pls help: 2. Evaluate the following . i log 10 + 10 3 ii 2 + 1 2 log 10 - 3 iii 2 log 5 + log 8 - 1 2 log 4 iv 2 log 10 3 + 3 log 10 - 2 - 1 3 log 5 - 3 + 1 2 log 4

Pls help:

2. Evaluate the following .
$(i) \log (10 + \sqrt[3]{10}) (ii) 2 + \frac{1}{2} \log (10^{- 3}) (iii) 2 \log 5 + \log 8 - \frac{1}{2} \log 4 (iv) 2 \log 10^{3} + 3 \log 10^{- 2} - \frac{1}{3} \log 5^{- 3} + \frac{1}{2} \log 4$