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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

## 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.

 Related Articles: Logarithm Table Properties of Logarithms Antilogarithm Tables Logarithm Calculator

## 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)

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## 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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