Solve the following logarithmic equation. log x+ log (x-99)=2

Deon Moran

Deon Moran

Answered question

2022-10-20

Solve the following logarithmic equation.
log x + log ( x 99 ) = 2

Answer & Explanation

Taxinov

Taxinov

Beginner2022-10-21Added 18 answers

Given
log x + log ( x 99 ) = 2
We know that property logarithmic function
log a x + log a y = log a ( x y ) log 10 ( x ) ( x 99 ) = 2 ( x ) ( x 99 ) = 10 2 x 2 99 x 100 = 0
Hence, solve quadratic equation we get solution of x
x 2 100 x + x 100 = 0 ( x 100 ) ( x + 1 ) = 0 x = 100 , 1

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