Question

Rajeev multiplies a number by 10, the log (to base 10) of this number will change in what way?

Answer 1

Let $x [\tex] be a positive number. Let [tex] y = 10x [\tex].</p><p>Then, [tex]log_{10}(y) = log_{10}(10x) = log_{10}(10) + log_{10}(x) = 1 + log_{10}(x).$

So the log to base 10 increases by 1.

Answer 2

Answer:

$\log_{10}(10x)=1+y$  

Step-by-step explanation:

Given : Rajeev multiplies a number by 10.

To find : The log (to base 10) of this number will change in what way?

Solution :

Let the number be 'x',

$y=\log_{10}x$ ....(1)

Now, take log 10x

$\log_{10}(10x)$

Applying logarithmic property, $\log(ab)=\log a+\log b$

$\log_{10}(10x)=\log_{10}10+\log_{10}x$

$\log_{10}(10x)=1+\log_{10}x$

$\log_{10}(10x)=1+y$ (From (1))

There is increase in a number by 1.