SOLUTION: Solve the following exponential equation. Write the answers as a decimal approximation (rounded to 2 decimal places)
9^(2x)=1657
Algebra.Com
Question 382247: Solve the following exponential equation. Write the answers as a decimal approximation (rounded to 2 decimal places)
9^(2x)=1657
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Take the log of both sides, any base you like.
\ =\ \ln(1667))
Use
\ =\ n\log_b(x))
to write:
\ =\ \ln(1667))
Solve by ordinary means:
}{2\ln(9)})
The rest is just calculator work.
Showing that
}{2\ln(9)}\ =\ \frac{\log_{10}(1667)}{2\log_{10}(9)})
to get an intuitive sense that my claim about the choice of log base being immaterial to the outcome is left as an exercise for the student.
John
My calculator said it, I believe it, that settles it
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