# How do you write each number as a power of the given base: 10; base 10?

Jan 11, 2018

No numbers were specified.
In general the number $\textcolor{b l u e}{n}$ can be written as a power of ten: ${10}^{{\log}_{10} \textcolor{b l u e}{n}}$

#### Explanation:

Except for values like $100$ or $100 , 000$ which are integer powers of $10$ ($100 = {10}^{2}$ and $100 , 000 = {10}^{5}$)
the necessary exponents can be approximated using a calculator or similar means.
By definition, if ${\log}_{10} n = q$ then ${10}^{q} = n$

For example, (here I used a spreadsheet builtin function since that was what was handy to evaluate ${\log}_{10}$ but some hand calculators could do this as well):

${\log}_{10} 47 = 1.6720978579$

So $47 = {10}^{1.6720978579}$

Jan 11, 2018

$1$

#### Explanation:

$\text{utilising the "color(blue)"law of logarithms}$

•color(white)(x)log_bx=nhArrx=b^n

$\Rightarrow {\log}_{10} 10 = n \Rightarrow 10 = {10}^{n}$

$\Rightarrow {10}^{1} = {10}^{n} \Rightarrow n = 1$

$\text{in general } {\log}_{b} \left(b\right) = 1$