Question

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

Answer 1

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?

Answer 2

I do not, could you please explain further?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

7/999
So that would equal 0.0070 correct?

Answer 7

yep!

Answer 8

Thank you!!