Question

How do you solve `ln x + ln (x+5) = ln 14`?

Answer 1

I found `x=2`

Explanation:

Use the property of the log:
`logx+logy=log(x*y)`
to get:
`ln[x(x+5)]=ln(14)`
for the logs to be equal the arguments must be equal as well, or:
`x(x+5)=14`
solve for `x`:
`x^2+5x-14=0`
Use the Quadratic Formula:
`x_(1,2)=(-5+-sqrt(25+56))/2=(-5+-sqrt(81))/2=(-5+-9)/2=`
two solutions:
`x_1=-7` NO it gives you a negative argument in the original logs.
`x_2=2` YES