Solve the equation.
Log(x+7)-logx=3
A) 3.5
B) 142.7
C) 0.0070
D) 0.0707

Question

Solve the equation.
Log(x+7)-logx=3
A) 3.5
B) 142.7
C) 0.0070
D) 0.0707

thefurball · Answer

There is a property with logarithms, which is$$\log(a) - \log(b) = \log(\frac{ a }{ b })$$Knowing that, we can simplify to $$\log(\frac{ x+7 }{ x }) = 3$$ Do you know how to solve from there?

anonymous · Answer

I do not, could you please explain further?

thefurball · Answer

Ok. To solve for logs you do $$\log(x) = y \rightarrow 10^{y} = x$$ so for our equation we get$$10^3 = \frac{ x + 7 }{ x }$$

anonymous · Answer

okay so I now have 1000=x+7 over x
would I move the x over?

thefurball · Answer

Yep! So you get$$1000x = x+7$$Then you can subtract x to get$$999x = 7$$Then?

anonymous · Answer

7/999
So that would equal 0.0070 correct?

thefurball · Answer

yep!

anonymous · Answer

Thank you!!