# how do you solve log 5 (0+1)-3?

## Expert Answers You need to evaluate the following logarithm `log_5 (0+1) - 3` , such that:

`log_5 (0+1) = log_5 1`

Since `log_5 1 = 0` yields:

`log_5 (0+1) - 3 = 0 - 3 = -3`

You may also evaluate the expression, such that:

`log_5 (0+1) - 3 = log_5 1 - 3*1`

Replace `log_5 5` for 1, such that:

`log_5 (0+1) - 3 = log_5 1 - 3*log_5 5`

Use the power property of logarithms, such that:

`log_5 (0+1) - 3 = log_5 1 - log_5 5^3`

Converting the difference of logarithms into the logarithm of quotient yields:

`log_5 (0+1) - 3 = log_5 1/(5^3)`

`log_5 (0+1) - 3 = log_5 (5^(-3)) `

Taking out the power of argument yields:

`log_5 (0+1) - 3 = -3log_5 5 = -3*1 = -3`

Hence, evaluating the given expression containing logarithms, yields `log_5 (0+1) - 3 = -3.`

Approved by eNotes Editorial Team

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