Question

What do you mean by log to the base e and log to the base 10? Give examples.
Explanation should be a detailed one​

Answer 1

Answer:

logarithms to Base 10 were used extensively for calculation up until the calculator was adopted in the 1970s and 80s. The concept of logarithms is still very important in many fields of science and engineering. One example is acoustics.

log button on calculator

Our calculators allow us to use logarithms to base 10. These are called common logarithms ("log" on a calculator). We normally do not include the 10 when we write logarithms to base 10.

We write

log x to mean log10 x.

[This is the convention used on calculators, so most math text books follow along. Note, however, that "log" in computer programming generally means "log base e", which we learn about on the next page.]

Examples

1. Find the logarithm of \displaystyle{5}{623}5623 to base \displaystyle{10}10. Write this in exponential form.

Answer

Using our calculator, we have:

\displaystyle \log{{5623}}={3.74997}log5623=3.74997

This means \displaystyle{10}^{3.74997}={5623}10

3.74997

=5623

Mental check: \displaystyle{10}^{3}={1},{000}10

3

=1,000 and \displaystyle{10}^{4}={10},{000}10

4

=10,000.

Our number \displaystyle{5623}5623 is between these values, so it's at least reasonable.

2. Find the antilogarithm of \displaystyle-{6.9788}−6.9788.

Answer

This means "if \displaystyle \log{{N}}=-{6.9788}logN=−6.9788, what is \displaystyle{N}N?"

Using the logarithm laws, \displaystyle{N}={10}^{ -{{6.9788}}}={0.000}{000}{105}N=10

−6.9788

=0.000000105

Answer 2

log to the base e of a number (ln) gives us the number to which e must be raised to get the given number

log to the base 10 of a number gives us the number to which 10 must be raised to get the given number

Generally, log to the base n of a number x gives the number to which n must be raised to get x

log$log_{n}x=y\\ n^{y}=x$

#BAL #answerwithquality