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Value of Log 1 to 10

In Mathematics, the inverse function of exponentiation is known as logarithmic functions or log functions. In this article, the value of log from 1 to 10 in terms of both common and natural logarithmic functions is explained in detail.

Logarithmic Function and its Types

The logarithm is defined as a quantity that represents the power in which the base (fixed number) is raised to produce a given number. The general representation of the logarithmic function is

f(x) = loga x

In general, the two different types of logarithmic functions are

  • Common Logarithmic Function
  • Natural Logarithmic Function

In common logarithmic function, the base of the logarithmic function is 10. Log10 or log represents this function.

In natural logarithmic function, the base of the logarithmic function is e. Loge or ln represents this function.

Value of Log 1 to 10 for Log Base 10

The value of log 1 to 10 ( common logarithm- log10 x) is listed here

Common Logarithm to a Number (log10 x) Log Value
Log 1 0
Log 2 0.3010
Log 3 0.4771
Log 4 0.6020
Log 5 0.6989
Log 6 0.7781
Log 7 0.8450
Log 8 0.9030
Log 9 0.9542
Log 10 1

Value of Log 1 to 10 for Log Base e

The value of log 1 to 10 in terms of the natural logarithm (loge x) is listed here.

Natural Logarithm to a Number (loge x) Ln Value
ln (1) 0
ln (2) 0.693147
ln (3) 1.098612
ln (4) 1.386294
ln (5) 1.609438
ln (6) 1.791759
ln (7) 1.94591
ln (8) 2.079442
ln (9) 2.197225
ln (10) 2.302585

Also, read:

Solved Examples

Example 1:

Find the value of log10(75/16) – 2 log10(5/9) + log(32/243).

Solution:

We know that loga mn = n loga m

 loga (p/q) = loga p – loga q

loga (mn) = loga m + loga n

using these logarithmic rules we have,

log10(75/16) – 2 log10(5/9) + log(32/243) = log10(75/16) – log10(5/9)2 + log(32/243)

= log10(75/16) – log10(25/81) + log(32/243) 

= log10 (75/16) – log10(25/81) + log(32/243)

= log10 [(75/16) × (32/243)] – log10 (25/81)

= log10 (50/81) – log10 (25/81)

= log10 [(50/81)/(25/81)]

= log10 [(50/81) × (81/25)]

= log10 2 = 0.3010

∴ log10(75/16) – 2 log10(5/9) + log(32/243) = 0.3010.

Example 2:

Evaluate log10 (124416).

Solution:

 log10 (124416) = log10 (512 × 243)

= log10 (29 × 35)

= log10 29 + log10 35

= 9 log10 2 + 5 log10 3

= 9 × 0.3010 + 5 × 0.4771

= 2.709 + 2.3855

= 5.0945

∴ log10 (124416) = 5.0945.

Example 3:

Find the value of log2 10.

Solution:

By the base change rule logb (a) = 1 / loga (b)

Thus log2 10 = 1 / log10 2

= 1 / 0.3010 = 3.3223.

Practice Problems

  1. What is the value of log10 80?
  2. If p = e280 and q = e300, prove that ln (ep2q –1) = 261.
  3. Solve for x: 5x= 2e5. (Hint: take natural logarithm on both sides)

To learn more values on common and natural logarithm, download BYJU’S – The Learning App and also learn maths shortcut tricks to learn with ease.

Frequently Asked Questions on Value of Log 1 to 10

What is the base of common logarithmic function?

The base of common logarithmic function is 10.

What is the value of log10 1 and ln 1?

The value of log10 1 = 0 and the value of ln 1 = 0.

What is the value of log 10?

The value of log10 10 is 1 whereas the value of loge 10 or ln 10 = 2.302585.

What is the value of log 10 base 2?

We know the change base rule of logarithms is logb a = 1/loga b. Thus log2 10 = 1/log10 2 = 3.3223.

What is the value of log 100 with base 10?

The value of log10 100 = log10 102 = 2 log10 10 = 2 × 1 = 2.

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