# Quick Logarithm Equation

• Apr 1st 2008, 01:36 PM
chrozer
Quick Logarithm Equation
How do you solve for $\displaystyle x$ in $\displaystyle log_5 x^4=2.5$?
• Apr 1st 2008, 01:38 PM
Jhevon
Quote:

Originally Posted by chrozer
How do you solve for $\displaystyle x$ in $\displaystyle log_5 x^4=2.5$?

$\displaystyle \log_5 x^4 = 2.5 \Longleftrightarrow 5^{2.5} = x^4$
• Apr 1st 2008, 01:48 PM
chrozer
Quote:

Originally Posted by Jhevon
$\displaystyle \log_5 x^4 = 2.5 \Longleftrightarrow 5^{2.5} = x^4$

How would you find the value of $\displaystyle x$ though?
• Apr 1st 2008, 01:49 PM
Jhevon
Quote:

Originally Posted by chrozer
How would you find the value of $\displaystyle x$ though?

take the fourth root of both sides, of course
• Apr 1st 2008, 01:55 PM
chrozer
Quote:

Originally Posted by Jhevon
take the fourth root of both sides, of course

Ok. Thnx!
• Apr 1st 2008, 01:59 PM
Jhevon
Quote:

Originally Posted by chrozer
Ok. Thnx...but how would you enter the fourth root of a value on a TI calculator?

there are several ways. i don't have a TI so let's do it the safe way. to take the fourth root means to raise to the 1/4 power.

so, $\displaystyle 5^{2.5} = x^4 \implies \pm (5^{2.5})^{1/4} = (x^4)^{1/4}$