# Simplify the following logarithms, evaluate if possible. a) log25-3 b) log3000 - log 30 Show all steps.

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Expert Answers

mvcdc | Certified Educator

1.

Simplify/Evaluate `log_2 5^(-3)`

One of the rules of logarithm is as follows:

`log_a b^x = x log_a b`

Hence, we can simplify the given expression to:

`-3log_2 5` or `3 log_2 (1/5)`

This cannot be simplified further, but evaluating using a calculator results to: -6.97

2.

`log3000 - log30`

We can express 3000 as `30*100`

Hence, `log3000 = log(30*100) = log30 + log100`

At this point, the expression we want to simplify is:

`log30 + log100 - log30`

`log30` simply cancels out leaving us with:

`log100`

But:

`log100 = log10^2 = 2log10 = 2`

(Here, since the base is not written, that means that the base of the operation is 10)