2020 AMC 12A Problems/Problem 10
There is a unique positive integer such thatWhat is the sum of the digits of
Any logarithm in the form .
Using property of addition, we can expand the parentheses into
Expanding the RHS and simplifying the logs without variables, we have
Subtracting from both sides and adding to both sides gives us
Multiplying by , raising the logs to exponents of base to get rid of the logs and simplifying gives us
Adding the digits together, we have ~quacker88