SOLUTION: write each of the following as a single logarithm a. 3In2+In (x^2)+2 answer 3In^2 b.1/2 loga 4-2 loga 5 answer loga4^1/2-log 5^2 can u please help me

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Question 235064: write each of the following as a single logarithm
a. 3In2+In (x^2)+2
answer 3In^2
b.1/2 loga 4-2 loga 5
answer loga4^1/2-log 5^2

can u please help me
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
write each of the following as a single logarithm
a. 3In2+In (x^2)+2
ln(9) + ln(x^2) + 2
ln[9x^2] + 2
Comment: 3ln^2 is not the answer to the problem you have posted.
---
answer 3In^2
------------------------------------------------
b.1/2 loga 4-2 loga 5
loga(4^1/2) - loga 5^2
----------------------------
= loga [2/25]
=========================
Cheers,
Stan H.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

a.

The first thing to do is look at the definition of a logarithm.

The base of the function is , so we can say that:

So we can now re-write your problem:

Now use:

To say:

and simplify to:

Now use the property that the sum of the logs is the log of the product, that is:

to write:

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b.

Use

To say:

Recall that:

To say:

Now use the property that the difference of the logs is the log of the quotient, that is:

To say:

John