1. Logarithmic Relationships

How would i solve this?

Log3^9-log3^27+log3^243

2. Re: Logarithmic Relationships

Originally Posted by strdatmage
How would i solve this?
Log3^9-log3^27+log3^243
There is nothing there to solve.
If you want to add those up then:
$\displaystyle 9L+27L+243L=~?$ where $\displaystyle L=\log(3)$

3. Re: Logarithmic Relationships

Originally Posted by Plato
There is nothing there to solve.
If you want to add those up then:
$\displaystyle 9L+27L+243L=~?$ where $\displaystyle L=\log(3)$
It says : Write each expression as a single logarithm. B. Find the value of each expression

4. Re: Logarithmic Relationships

Originally Posted by strdatmage
It says : Write each expression as a single logarithm. B. Find the value of each expression
That is exactly what I posted.
Now you do some work for yourself.

5. Re: Logarithmic Relationships

Okay, so just Do that and replace L With 3?

6. Re: Logarithmic Relationships

Originally Posted by strdatmage
It says : Write each expression as a single logarithm. B. Find the value of each expression
As Plato demonstrated, you can use this property of logarithms:

$\displaystyle \log_bx^a=a\log_bx,\quad x>0, b>0, b\ne1$.

Then combine like terms. You should familiarize yourself with basic logarithmic identities. Consult your textbook for information.

7. Re: Logarithmic Relationships

Originally Posted by strdatmage
How would i solve this?

Log3^9-log3^27+log3^243
I'm a little bit confused about the writing of this sum ...

Could it be that the original term was:

$\displaystyle \log_3(9) - \log_3(27) + \log_3(243)$

If so the final result is 4.

8. Re: Logarithmic Relationships

Originally Posted by strdatmage
It says : Write each expression as a single logarithm. B. Find the value of each expression
9L + 27L + 243L = 279L; where L = log(3)

279log(3) is the single logarithm
Use your calculator to find the value the appropriate base as it wasn't detailed here (assuming base e or base 10)