In mathematics, a logarithm is the inverse function of exponentiation. It is another way of writing exponents.  A logarithm is the power to which a base must be raised to yield a given number. For example, the logarithm of 1,000 with a base of 10 is 3 because 10 raised to the third power equals 1,000.  Here are some examples of logarithms: Folding paper: How many times you need to fold a sheet of paper to get 64 layers Measuring molecules: How many molecules from the original liquid are left after a C dilution Sound intensity: How much power is needed to increase a speaker's volume by 10... Show more

In mathematics, a logarithm is the inverse function of exponentiation. It is another way of writing exponents. 

A logarithm is the power to which a base must be raised to yield a given number. For example, the logarithm of 1,000 with a base of 10 is 3 because 10 raised to the third power equals 1,000. 

Here are some examples of logarithms:
Folding paper: How many times you need to fold a sheet of paper to get 64 layers
Measuring molecules: How many molecules from the original liquid are left after a C dilution
Sound intensity: How much power is needed to increase a speaker's volume by 10 decibels (dB) 

There are two types of logarithms:
Common logarithm: Also called the base 10 logarithm, it is represented as log10 or simply log.
Natural logarithm: Also called the base e logarithm, it is represented as ln or loge. 

Logarithms are used in linear regression and to make graphs of exponential data easier to interpret. 

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Algebra Practice Test: Logarithm

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25 Questions

1. Log 20 + log 30 log 36 = 2X, then X is =

210013/2

2. What is the value of Log264

58log y6

3. Log (x + 3) – log (x - 3) = 1.

73-1211/3

4.

2Log 1Log abc0

5. If log 2 = 0.30 and log 3 = 0.48, find log 36

1.440.33cannot be found0.45

6. Given that Log103 = 0.4771, the value of Log10810 is:

3.1902.19019.0842.019

7. [log1010000 + log10100000] is:

4956

8. If log 2 = 1 and log 3 = b, find the value of log 2.25

b - 2a - b 2b - 2aa2 + b2

9. If log 5 = 0.699 and log 6 = 0.778 then what is the value of log 12?

none of these.1.4771.0791.113

10. Which one is correct?

log a + log b = log (a +Log10Log10 10 =1(c) log (m × n) = (log m × log n)log (1 + 2 + 3) = log 1 + log 2 + log 3

11. The value of Log100.07 lies between:

2 and d -10 and 1-2 and -30 and -1

12. Log1728 to the base () is equal to:

11936

13. Find the value of the expression without logs: 2 log x – log y = 1

10/(x − y)10/(2x – y)x - 3yx = 10 y

14. Value of Log101 is:

010.010.1

15. log27 is:

a rational numbera prime numberan integeran irrational number

16. Solve for x:2 log x + 1 = log 250.

25cannot be found05

17. If x = Log (a2 /bc), y = Log ((b)2/ac) and z = Log (c2/ab), find the value of x + y + z.

zerolog (a)log (ab(c)1

18. Find x in the equation:log (x 2) + log (x + 2) = log 5.

3246

19. Find the value of the expression log 5 + log 8 - 2 log 2 = ?

11000a+b+c

20. Find the value of the expression: log 8 + log 25 + 2 log 3 - log 18 = ?

110020

21. Solve for x:log (x 21) = 2.

111217-3

22. If log a + log b = log (a+b) then b = ?

a2a/(a − 1)a1

23. If Log32X = 0.8, then 2x = ?

321621

24. Find the value of Log264 = ; then x =

2 4636

25. If log7(X2 + x) - log7(x2 + 1) = 2, then the value of is:

9128327