Logarithmic Relationships

How would i solve this?

Log3^9-log3^27+log3^243

Re: Logarithmic Relationships

Quote:

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 $\displaystyle L=\log(3)$

Re: Logarithmic Relationships

Quote:

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

Re: Logarithmic Relationships

Quote:

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.

Re: Logarithmic Relationships

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

Re: Logarithmic Relationships

Quote:

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.

Re: Logarithmic Relationships

Quote:

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.

Re: Logarithmic Relationships

Quote:

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)