Logs

• Sep 28th 2011, 07:01 PM
habibixox
Logs
Solve for http://webwork.rutgers.edu/webwork2_...dd0b8b8e91.png:
Is what I'm doing against rules of math:

3^3 = log base 3 x
27 = log base 3 x
27= 3^x

log 27 = x log 3

x = log 27/ log 3? x=3

I think that's wrong.
• Sep 28th 2011, 07:21 PM
Amer
Re: Logs
\$\displaystyle \log_3 (\log_3 x) = 3 \$

\$\displaystyle \log_3 x = 3^3 \$

\$\displaystyle x = (3^3)^3 \$
• Sep 28th 2011, 10:22 PM
Prove It
Re: Logs
Quote:

Originally Posted by Amer
\$\displaystyle \log_3 (\log_3 x) = 3 \$

\$\displaystyle \log_3 x = 3^3 \$

\$\displaystyle x = (3^3)^3 \$

I'm sure you mean \$\displaystyle \displaystyle x = 3^{3^3}\$...
• Sep 29th 2011, 08:01 AM
HallsofIvy
Re: Logs
An important distinction! \$\displaystyle (3^3)^3= 9^3= 729\$. \$\displaystyle 3^{3^3}= 3^{27}= 7625597484987\$!
• Sep 29th 2011, 08:48 AM
Quacky
Re: Logs
Quote:

Originally Posted by HallsofIvy
An important distinction! \$\displaystyle (3^3)^3= 9^3= 729\$

Are you sure?
• Sep 29th 2011, 09:59 AM
Deveno
Re: Logs
\$\displaystyle (3^3)^3 = 3^9 = 19,683\$