Evaluate the expression.

The point here, sally1, is that we don't need a calculator for ANY of them....!!! We're just using some log properties to evaluate them.....here's the second one....

2) log₅ 0.2    ..... this one looks tricky, but let's remember something...that 0.2 = 2/10 = 1/5

And we can write 1/5   as  5^-1   (remember that ??)

So we have.......

log₅ 5^-1  and by a  log property, we can bring the -1 out front  ..... and we have.....

(-1)log₅ 5    ....and log₅ 5  = 1  ...so we have....

(-1)(1)  = -1   

3) These used to give me trouble...once you see the 'trick,' it's easy......let me give you an example...let's say we have 

2 ^{log₂ 4}          

Note that log₂ 4   just asks..what power do we need to raise 2 to to get 4???  The answer is 2

So we really have

2²  = 4      Note that this was just the last number in the original exponent!!!

In general   when we have  .....a ^{log_a b}  the answer is just "b".....this is one you may have to think about a little bit!!!

So.....in your problem  5 ^{log₅ 19}    ...the answer is just "19"

4) e ^{ln √11}   Note that there is a little "e" implied here  we can write this as

e ^{ln_e √11}      And we have the same situation as the previous problem!!!

The answer is just "√11"

Lastly

5)  ln (1/e)  = ln (e) ^-1     and by a property of exponents we can bring the -1 to the front

So we have

(-1) ln e        and ... ln e  = 1  ...   so we have

(-1)(1) = -1

And that's it!!!

1)  Note that √9 = 9 ^1/2    ....so we have...

Log ₉ 9 ^1/2 .... and by a property of logs, we can bring the 1/2 in front of the expression..so...

1/2 Log ₉ 9 .....and  Log ₉ 9  = 1  ....so we have

1/2 * 1  = 1/2

For the log problems I'm trying to put it into the calculator but the answers are not coming out right. 

That's probably because you're trying to use base 10......most of these (like the first one, for instance) are using a different base.

So how would I be able to evaluate it?

Thank you so much. Now, I'm about to go and try to work some out on my own. Thanks for your help.