Question 11

If $\ln x+\ln (x-5)=\ln (3 x)$, then $x=$
Question Help:
Video
Submit Question

Answer

Expert–verified

Hide Steps

Answer

$\boxed{x = 8}$

Steps

Step 1 ：$\ln [x(x-5)] = \ln (3x)$

Step 2 ：$x(x-5) = 3x$

Step 3 ：$x^2 - 5x = 3x$

Step 4 ：$x^2 - 8x = 0$

Step 5 ：$x(x - 8) = 0$

Step 6 ：$x = 0$ or $x = 8$

Step 7 ：Substitute $x = 0$ back into the original equation, it does not satisfy the equation because the natural logarithm is undefined for zero.

Step 8 ：$\boxed{x = 8}$