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

2 Answers
Alan P.
Jan 11, 2018

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#

Jim G.
Jan 11, 2018

#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#

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