Question

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

Answer 1

No numbers were specified.
In general the number `color(blue)n` can be written as a power of ten: `10^(log_10 color(blue)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`

Answer 2

`1`

Explanation:

`"utilising the "color(blue)"law of logarithms"`

`•color(white)(x)log_bx=nhArrx=b^n`

`rArrlog_(10)10=nrArr10=10^n`

`rArr10^1=10^nrArrn=1`

`"in general "log_b(b)=1`