$$2{\log _{10}}^5 + $$ $${\log _{10}}8 \,- $$ $$\frac{1}{2}{\log _{10}}4$$ = ?
A. 2
B. 4
C. $${\text{2 - 2 lo}}{{\text{g}}_{10}}^2$$
D. $${\text{4 - 4 lo}}{{\text{g}}_{10}}^2$$
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & 2{\log _{10}}5 + {\log _{10}}8 - \frac{1}{2}{\log _{10}}4 \cr & = {\log _{10}}\left( {{5^2}} \right) + {\log _{10}}8 - {\log _{10}}\left( {{4^{\frac{1}{2}}}} \right) \cr & = {\log _{10}}25 + {\log _{10}}8 - {\log _{10}}2 \cr & = {\log _{10}}\left( {\frac{{25 \times 8}}{2}} \right) \cr & = {\log _{10}}100 \cr & = 2 \cr} $$Related Questions on Logarithm
Which of the following statements is not correct?
A. log10 10 = 1
B. log (2 + 3) = log (2 x 3)
C. log10 1 = 0
D. log (1 + 2 + 3) = log 1 + log 2 + log 3
$${{\log \sqrt 8 } \over {\log 8}}$$ is equal to:
A. $$\frac{1}{6}$$
B. $$\frac{1}{4}$$
C. $$\frac{1}{2}$$
D. $$\frac{1}{8}$$
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