1. ## Need help with Log please

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

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

3. 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?
$\displaystyle b^{\log_bx}=x$

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

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.