Question

Solve the following logarithmic equation.In (x+5) + In (x-2) = 2 In x. Simplofy your answer. Type an integer or a fraction. Use a comma to separate answers as needed.

Answer 1

you know how the log addition works right?

Answer 2

use ln(a) +ln(b) = ln(ab)

Answer 3

and that ln(x) is defined only on x>0

Answer 4

x=10/3. Do I need to detail the solution?

Answer 5

Ok, \[\ln (x-5) + \ln(x+2)=\ln(x^2)\]
then\[\ln(x-5) +\ln (x+2)-\ln(x^2)=0\]
\[\ln(((x-5)*(x+2))/(x^2))=0\]
\[x^2+3x-10=e^0*x^2\]
\[3x=10\]
Finally\[x=10/3\]