Expert Answer to "How do you solve for x?: log⁡(x)+log⁡(x−9)=1"

Jackson David

Answered question

2022-02-05

How do you solve for x?:

\log (x) + \log (x - 9) = 1

gogrervisulget9z

Beginner2022-02-06Added 12 answers

Step 1
using the laws of logarithms

\log \log y = \log (x y)

\log_{b} x = n \Leftrightarrow x = b^{n}

note that

\log x \equiv \log_{10} x

\Rightarrow \log_{10} x (x - 9) = 1

\Rightarrow x^{2} - 9 x = 10^{1} = 10

\Rightarrow x^{2} - 9 x - 10 = 0 \leftarrow

in standard form

\Rightarrow (x - 10) (x + 1) = 0

\Rightarrow x = 10

x = - 1

note that

x > 0

and

x - 9 > 0

\Rightarrow x = - 1

is invalid

\Rightarrow x = 10

is the solution

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?