# Thread: combining/simplifying logs (part 1)

1. ## combining/simplifying logs (part 1)

Heres what i did so far:

brought the constants in front of the logs into the log as exponents according to the law of log.

not sure how to proceed from here, since the 3rd part is log_10_Z over 2. Im not sure how to properly take care of such numbers in an equation which is primarily filled with logs. Im posting a similiar question (but perhaps a bit tougher) now.

Thank you.

2. Originally Posted by Evan.Kimia

Heres what i did so far:

brought the constants in front of the logs into the log as exponents according to the law of log.

not sure how to proceed from here, since the 3rd part is log_10_Z over 2. Im not sure how to properly take care of such numbers in an equation which is primarily filled with logs. Im posting a similiar question (but perhaps a bit tougher) now.

Thank you.
$\frac{log_{10} Z}{2} = \frac{1}{2}log_{10} Z$

You can treat the half just like the other powera

3. Ah, thank you. So I would get log_10_((y^-4)(x^3)(Z^1/2))

4. Originally Posted by Evan.Kimia
Ah, thank you. So I would get log_10_((y^-4)(x^3)(Z^1/2))
Yes although it would be more proper to write it as $log_{10} \left(\frac{x^3 \sqrt{Z}}{y^4}\right)$