• Dec 5th 2008, 11:06 AM
Jenne
Hi I am having a hard time understanding logs in class can someone help?

1.
I am to find the exact value for this
How would I start

2^log base2 7

Am i to transform this somehow first?

2.Another one is logbase6 6^74 for this one I got a 74 it is right but why? its juse the exponent of the 6
• Dec 5th 2008, 11:41 AM
running-gag
Quote:

Originally Posted by Jenne
Hi I am having a hard time understanding logs in class can someone help?

1.
I am to find the exact value for this
How would I start

2^log base2 7

Am i to transform this somehow first?

2.Another one is logbase6 6^74 for this one I got a 74 it is right but why? its juse the exponent of the 6

\$\displaystyle log_2 7\$ is the real x such as \$\displaystyle 2^x = 7\$
Therefore \$\displaystyle 2^{log_2 7} = 7\$

In the same way
\$\displaystyle log_6 {6^{74}}\$ is the real x such as \$\displaystyle 6^x = 6^{74}\$
Therefore \$\displaystyle log_6 {6^{74}} = 74\$
• Dec 5th 2008, 11:48 AM
masters
Quote:

Originally Posted by Jenne
Hi I am having a hard time understanding logs in class can someone help?

1.
I am to find the exact value for this
How would I start

2^log base2 7

Am i to transform this somehow first?

\$\displaystyle b^{\log_bx}=x\$

\$\displaystyle 2^{\log_27}=7\$

Quote:

Originally Posted by Jenne
2.Another one is logbase6 6^74 for this one I got a 74 it is right but why? its juse the exponent of the 6

\$\displaystyle \log_b b^x=x\$

\$\displaystyle \log_6 6^{74}=74\$

Just some more properties of logarithms. See here: Logarithmic Properties
Enjoy.