Common Logarithms

Problem: 1

Find log 1000 without using a calculator.

Problem: 3

Find log 0.0001 without using a calculator.

Problem: 5

Find log 100 without using a calculator.

Problem: 7

Find the value of x:

log x = 1.5

Problem: 9

Compute the value of log 5 and round the result to two decimal places.

Problem: 11

Find the value of log(3.5)

given that log(3500) = 3.544.

Problem: 13

Find the characteristic of log(3500) given that

log(3500) = 3.544.

Problem: 15

Find the mantissa of log0.035, given that log(3500) = 3.544.

Problem: 17

Graph y = 10^x and y = log x on the same set of axes. Trace along the curve y = log x and find the value of y when x = 1.

Problem: 19

How can you determine the integer closest to log 0.034 without using a calculator?

Problem: 21

Find the approximate value of the common logarithm of 10,016 from the given choices without using a calculator.

(a) 5 (b) 3 (c) 4 (d) 6

Problem: 23

In a concert, the intensity of music was reported to be 80 decibels. The minimum intensity of sound detectable by human ear, I₀, is 1 decibel. Find how many times the minimum detectable intensity this music was. Use the formula:

Problem: 25

The pH value of blood is 7.4. Find the concentration of hydrogen ions in it.

Use the formula pH = –log(H⁺), where H⁺ is the concentration of hydrogen ions (in moles/liter) of the solution.

Problem: 27

The magnitude of earthquakes is denoted by a value on Richter scale. The Richter scale is a logarithmic scale in which the value x corresponds to a measured amplitude of K. 10^x, where the constant K depends on the units being used to measure the quake.

If in a city, the Richter's magnitudes registered are 7.5 and 6.7 in two consecutive years, find the ratio of the measured magnitudes.