Simplify the expression \(log_{10}18 - log_{10}2.88+log_{10}16\)

  • A 31.12
  • B 3.112
  • C 2
  • D 1
waec 2005mathematics

The correct answer is C. 2

\(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\)

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