Jump to content
Wildan Bagus W

Nilai $x$

Recommended Posts

Pada bentuk logaritma $\log_ab=c$, $a$ disebut bilangan pokok atau basis, $b$ disebut numerus, dan $c$ adalah hasil logaritma. Nilai numerus harus positif. \begin{align*}\log_2\left(\log_4x\right)&=\log_4\left(\log_2x\right).\end{align*} Syarat (1): $x>0$.
Syarat (2): $\log_4x>0\implies x>1$.
Syarat (3): $\log_2x>0\implies x>1$.
Irisan dari ketiganya adalah $x>1$. \begin{align*}\log_2\left(\log_4x\right)&=\log_4\left(\log_2x\right)\\\log_2\left(\log_4x\right)&=\log_2\sqrt{\log_2x}\\\log_4x&=\sqrt{\log_2x}\\\frac{1}{2}\log_2x&=\sqrt{\log_2x}\rightarrow\text{Misal }\log_2x=a\\\frac{1}{2}a&=\sqrt{a}\\a(a-4)&=0\\\rightarrow&\begin{cases}a=0\implies\log_2x=0\implies x=1\text{ (tidak memenuhi)}\\a=4\implies\log_2x=4\implies x=\boxed{16}\end{cases}.\end{align*}

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now


×