Question

How do you calculate $\log 5.14$ ?

Answer 1

Hint: In this problem we have been given a logarithmic value and we are asked to calculate the given log of some decimal value. We can do this by using a calculator or we can use the logarithmic table to calculate the given log of decimal value.

Complete step-by-step solution:
We have been asked to calculate $\log 5.14$ .
The common logarithm is the logarithm with base $10$ . It is also known as the decadic logarithm and as the decimal logarithm, named after its base. This is the default base of a log or the standard logarithm. It is indicated by $\log \left( x \right)$ , ${\log _{10}}\left( x \right)$ or sometimes $Log\left( x \right)$ with a capital L.
In this problem, we are going to use the given log base as $e$ . And then we proceed.
We guess the only way to calculate $\log 5.14$ by using a calculator. Note that you might need a scientific or a graphic calculator, because those calculators are the only ones that have the logarithmic options.
On calculators, it is printed as $\log $ , but mathematicians usually mean natural logarithm that is logarithm with base $e \approx 2.71828$ .

So, $\log 5.14 \approx 0.71$

Additional Information: General procedure for determining logarithms of numbers less than $1$ : Determining the mantissa of the number as if it were between $1$ to $10$ , using the L scale. Then subtract the characteristic for the number of places the decimal point of our actual number is to the left of the whole single digit number. Usually there are two different buttons on calculators, one saying log which is base ten and one saying $\ln $ which is a natural log base $e$ . It is always assumed, unless otherwise stated, that $\log $ means ${\log _{10}}$ . Logs are read aloud as$\log $, natural$\log $, $\ln $ or log base whatever.

Note: The logarithm or log is the inverse of the mathematical operation of exponentiation. This means that the log of a number is the number that a fixed base has to be raised to in order to yield the number. In this problem we considered the given $\log $ base as $10$ .