# Thread: Quick Logarithm Equation

1. ## Quick Logarithm Equation

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

2. Originally Posted by chrozer
How do you solve for $\displaystyle x$ in $\displaystyle log_5 x^4=2.5$?
$\displaystyle \log_5 x^4 = 2.5 \Longleftrightarrow 5^{2.5} = x^4$

3. 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?

4. Originally Posted by chrozer
How would you find the value of $\displaystyle x$ though?
take the fourth root of both sides, of course

5. Originally Posted by Jhevon
take the fourth root of both sides, of course
Ok. Thnx!

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