Question

If log 2 =0.3010 and log 7 = 0.8451, then find the value of log 2.8

Answer 1

Answer:

0.4471

Step-by-step explanation:

• log(2.8)=log(28/10)=log(4*7/10)
• log(4*7/10) = log(4*7)-log(10) {log(a/b) =log(a) - log(b)}
• log(4)+log(7)-log(10) {log(a*b) =log(a) + log(b)}
• 2log(2) + log(7) - log(10)
• =2*(0.3010) + 0.8451 - 1
• =0.4471

Answer 2

The value of log 2.8 is 0.4471

Given : The given values are, log 2 =0.3010 and log 7 = 0.8451

To find : The value of log 2.8

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of log 2.8)

Here, we will be using the general formula of logarithm. (and, in this case we will be assuming that all the log have 10 as their bases)

Now,

$= log(2.8)$

$= log( \frac{28}{10} )$

$= log(28) - log(10)$

$= log(4 \times 7) - log(10)$

$= log(4) + log(7) - log(10)$

$= log( {2})^{2} + log(7) - log(10)$

$= [2 \times log(2)] + log(7) - log(10)$

$= (2 \times 0.3010) + 0.8451 - 1$

$= 0.4471$

(This will be considered as the final result.)

Used formula :

• $log_{a}(x) + log_{a}(y) = log_{a}(xy)$
• $log_{a}(x) - log_{a}(y) = log_{a}( \frac{x}{y} )$
• $log_{a}( {x}^{n} ) = n \times log_{a}(x)$
• $log_{10}(10) = 1$

Hence, the value of log 2.8 is 0.4471