Question

How do you solve `log_10(x+7) - log_10(x-7)=1`?

Answer 1

Part solution given. It has been taken to a point that is much easier to solve.

Explanation:

You are dealing with logs in that the `color(blue)("all")` of the left is logs. Consequently the value on the right is a value obtained from taking a log

Let b be a constant
Write the right hand side as :
`-> log_10(b)=1`

`10^1 = b" so " b=10`

Subtraction of logs is the consequence of division of the source values. So now we have:

`(x+7)/(x-7)=10`

`=> x+7 = 10x -70`

I will let you take over from this point and complete the calculations.