Question

solve for x :
log(3x+7)+log(x-2)=1show work plzz....i need to understand how to do this

Answer 1

are these log base e or 10?

Answer 2

Log base 10 makes more sense.
Combine logs using the property that log(a)+log(b)=log(ab)
\[\log((3x+7)(x-2))=1\]
Raise everything by 10.
\[(3x+7)(x-2)=10^1\]
So:
\[3x^2+7x-6x-14=10\]
\[3x^2+x-24=0\]
Which factors to:
\[(3x-8)(x+3)=0\]
So x=8/3 and -3

Answer 3

thanks a bunch

Answer 4

No problem :P