Simplify the expression log 10 18 - log 10 2 88... - WAEC Mathematics 2005 Question
Simplify the expression \(log_{10}18 - log_{10}2.88+log_{10}16\)
A
31.12
B
3.112
C
2
D
1
correct option: c
\(log_{10}18 - log_{10}2.88+log_{10}16\
=log_{10}18 - log_{10}\left(\frac{288}{100}\right)+log_{10}16 = log_{10}\left(\frac{18\times 16}{1}\times \frac{100}{288}\right)\
=log_{10}\left(\frac{288\times 100}{288}\right)=log_{10}100=log_{10}10^2=2log_{10}10=2\)
=log_{10}18 - log_{10}\left(\frac{288}{100}\right)+log_{10}16 = log_{10}\left(\frac{18\times 16}{1}\times \frac{100}{288}\right)\
=log_{10}\left(\frac{288\times 100}{288}\right)=log_{10}100=log_{10}10^2=2log_{10}10=2\)
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