Question

How do you solve `log516 - log52t = log52`?

Answer 1

Remember the logarithm rule: `log_(a)(x/y)=log_ax-log_ay`
You can work in reverse:
`log516-log52t=log52`
`log(516/(52t))=log52`

Now, there are multiple things you could do from here, but the easiest would be to recognize that if `loga=logb,a=b`.
Therefore, `516/(52t)=52`.
We can solve for `t`.
`516=2704t^2`
`516/2704=t^2`
`sqrt(516/2704)=t`
`sqrt(129/676)=t`

Notice that we only use the positive square root, excluding `-sqrt(129/676)`. We must do this since if we plugged`-sqrt(129/676)` into `log52t`, we would get a negative number, which is impossible.