How do you solve log x - log 10= 14?

Mar 12, 2018

$x = {10}^{15}$

Explanation:

We make use of two identities, one - $\log a - \log b = \log \left(\frac{a}{b}\right)$ and if $\log u = v$, then $u = {10}^{v}$

Using them we can write $\log x - \log 10 = 14$ as

$\log \left(\frac{x}{10}\right) = 14$

or $\frac{x}{10} = {10}^{14}$

i.e. $x = 10 \times {10}^{14} = {10}^{15}$