Logarithmic functions

Logarithmic functions > Logarithms

12345Logarithms

Exercises

Exercise 1

Which of the following logarithms are easy to evaluate without the help of a calculator? Calculate these logarithms. Determine the other ones rounded to two decimals.

${}^{4} log (64)$

${}^{4} log (400)$

${}^{\frac{1}{3}} log (60)$

${}^{\frac{1}{3}} log (81)$

${}^{\frac{1}{3}} log (\frac{1}{81})$

${}^{0.1} log (1000000)$

Exercise 2

For each of the following logarithms, indicate between which two consecutive whole numbers you expect them to lie.

${}^{6} log (30)$

${}^{3} log (70)$

${}^{\frac{1}{2}} log (10)$

${}^{\frac{1}{3}} log (0.01)$

Exercise 3

Approximate the following logarithms to three decimals.

${}^{2.5} log (100)$

${}^{0.7} log (20)$

${}^{2.3} log (0.05)$

${}^{15.2} log (2.3)$

Exercise 4

For each of the following equations, write the solutions as a logarithm. Then approximate the logarithm to one decimal.

$10 \cdot 10^{x} = 0.1$

$0.5 \cdot 2^{x} = 30$

$54 \cdot {0.8}^{t} = 27$

Exercise 5

A bacterial colony grows exponentially at a rate of $2$ per hour.

Calculate how many minutes it will take for the colony to triple in size. Use logarithms in your calculation.

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