`log_10(t - 3) = 2.6` Solve the equation accurate to three decimal places

In solving a logarithmic equation, we may simplify using logarithm properties.

Recall the logarithm property: `a^((log_(a)(x))) = x` .

When we raise the log with the same base, the "log" will cancel out.

This is what we need to accomplish on the left side.

 The problem `log_(10)(t-3)=2.6` has a logarithmic base of 10.

That is our clue to raise both sides by base of 10.

`10^(log_10(t-3))=10^(2.6)`

`t-3 =10^(2.6)`

`+3 +3`

-----------------------

`t = 10^(2.6) +3`

`t~~401.107`

To check, plug-in the value of `t=401.107 ` in` log_(10)(t-3)` :

`log_(10)(401.107-3)`

`log_(10)(398.107)`

`= 2.599999814~~2.6 ` 

So, 

`t ~~401.107` is a real solution.