Question

1. Which are true of x = log10 31,500? Select all that apply.

Answer 1

Given:

$x=\log_{10}31,500$

To find:

Select the true statements from the given options about the given value.

Solution:

We have,

$x=\log_{10}31,500$

It can be written as

$x=\log_{10}(2^23^25^37)$

$x=\log_{10}(2^2)+\log_{10}(3^2)+\log_{10}(5^3)+\log_{10}(7)$     $[\because \log(ab)=\log a+\log b]$

$x=2\log_{10}2+2\log_{10}3+3\log_{10}5+\log_{10}(7)$

$x=2\left(0.30105\right)+2\left(0.47712\right)+3\left(0.69897\right)+0.8451$

$x=4.49835$

Clearly, the value of x lies between 4 and 5. So, $x>4$ and $x$.

Therefore, the correct options are C and D.