Chapter 14

Evaluate (a) \(\log _{3} 9\) (b) \(\log _{10} 10\) (c) \(\log _{16} 8\)

Evaluate (a) lg 0.001 (b) lne (c) \(\log _{3} \frac{1}{81}\)

Solve the following equations: (a) \(\lg x=3\) (b) \(\log _{2} x=3\) (c) \(\log _{5} x=-2\)

Write (a) \(\log 30\) (b) \(\log 450\) in terms of \(\log 2\), \(\log 3\) and \(\log 5\) to any base.

Write \(\log \left(\frac{8 \times \sqrt[4]{5}}{81}\right)\) in terms of \(\log 2, \log 3\) and \(\log 5\) to any base.

Simplify } \log 64-\log 128+\log 32

Evaluate } \frac{\log 25-\log 125+\frac{1}{2} \log 625}{3 \log 5}

Solve the equation: $$ \log (x-1)+\log (x+1)=2 \log (x+2) $$

Solve the equation \(2^{x}=3\), correct to 4 significant figures. Taking logarithms to base 10 of both sides of \(2^{x}=3\) gives:

Solve the equation \(2^{x+1}=3^{2 x-5}\) correct to 2 decimal places.

Solve the equation \(x^{3.2}=41.15\), correct to 4 significant figures.