How do I solve for $k$ in the following equation?
$$\log _{10}4 = 2k$$
I expect that the solution will be pretty simple, yet I can't seem to figure it out.
Asked
Active
Viewed 358 times
0
-
2just divide by $2$ both side – FFjet Aug 30 '19 at 15:09
-
4You can simplify $\log_{10} 4$ – Kitter Catter Aug 30 '19 at 15:10
-
1Hey thanks @Kitter – Synchrowave Aug 30 '19 at 15:12
-
2@Synchrowave sure, let me know if you need help with that portion, but you might know how to do it from the properties of log. – Kitter Catter Aug 30 '19 at 15:13
2 Answers
5
If $2k=\log_{10} 4,$ then $k=\dfrac{\log_{10}4}2$.
Furthermore, $\log_{10}4=\log_{10}2^2=2\log_{10}2$, so $k=\log_{10}2$.
J. W. Tanner
- 60,406
3
Obviously, $k=\dfrac{1}{2}\log_{10} 4$, but we can further simplify it.
By using the identity $b\log a=\log a^b$, $k=\log_{10} 4^\frac{1}{2}=\boxed{\log_{10} 2}$
MafPrivate
- 4,033