Asked by Anonymous
find the values of x which satisfy the equation log_10(x^2+4) = 2+log_10 x-log_10 20
Answers
Answered by
mathhelper
If the base of your log is 10, we don't have to write the base, so ...
log(x^2+4) = 2 + log x - log 20
log(x^2 + 4) - log x + log 20 = 2
log( 20(x^2 + 4)/x ) = log 100
20(x^2 + 4)/x = 100
(x^2 + 4)/x = 5
x^2 + 4 = 5x
x^2 - 5x + 4 = 0
(x - 1)(x - 4) = 0
x = 1 or x = 4
log(x^2+4) = 2 + log x - log 20
log(x^2 + 4) - log x + log 20 = 2
log( 20(x^2 + 4)/x ) = log 100
20(x^2 + 4)/x = 100
(x^2 + 4)/x = 5
x^2 + 4 = 5x
x^2 - 5x + 4 = 0
(x - 1)(x - 4) = 0
x = 1 or x = 4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.