# Calculate without using calculator: log 25 + log 40

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### 4 Answers

Calculate without using a calculator log 25 + log 40

On of the rules of logarithms says that the sum of two logs is equal to the log of the product of the two numbers - therefore

log 25+log 40 = log (25*40) = log 1000

Since these logrithms are base 10 we want to write 1000 as 10 raised to some number and the number it is raised to is the answer.

since 10*10=100 and 100*10=1000 we know 1000=10^3

This means that log 1000 = 3 and therefore that log 25+log 40=3

log 25 + log 40

Using the properties with know that:

log x + log y = log x*y

==> log 25 + log 40 = log 25*40

= log 1000

= log 10^3

= 3 log 10

= 3*1 =3

**The answer is 3.**

### User Comments

The value of log 25 + log 40 has to be determined.

Use the property of logarithm log a + log b = log(a*b). This gives:

log 25 + log 40

= log(25*40)

= log 1000

= log 10^3

Use the property log a^b = b*log a, which gives:

3*log 10

Now log is logarithm to the base 10, use the property log_b b = 1

This gives log 10 = 1 or 3*log 10 = 3

Therefore the value of log 25 + log 40 = 3

log 40 + log 25

=log (25X40)

=log 1000

=3