# Logaritma

## Sifat logaritma 1

###### Hubungan Eksponen dan Logaritma

Hubungan eksponen dan logaritma

$$^a\log b = c \rightarrow a^c = b$$

$$a > 0, \: b > 0$$ dan $$a \neq 1$$

Sifat Logaritma 1

$$^a \log c^p = p \:.\: ^a \log c$$

$$^{a^q} \log c = \frac{1}{q} \:.\: ^a \log c$$

$$^{a^q} \log c^p = \frac{p}{q} \:.\: ^a \log c$$

Contoh 01

Tentukan nilai x dariĀ $$^2 \log x = 3$$

\begin{equation*} \begin{split} & ^2 \log x = 3 \\\\ & x = 2^3 \\\\ & \bbox[5px, border: 2px solid magenta] {x = 8} \end{split} \end{equation*}

Contoh 02

\begin{equation*} \begin{split} & ^7\log \frac{1}{49} \\\\ & ^7\log 7^{-2} \\\\ & -2 \:.\: ^7\log 7 \\\\ & \bbox[5px, border: 2px solid magenta] {-2} \end{split} \end{equation*}

Contoh 03

\begin{equation*} \begin{split} & ^8\log 2 \\\\ & ^{\large{2^3}}\log 2 \\\\ & \frac{1}{3}\:.\: ^2 \log 2 \\\\ & \bbox[5px, border: 2px solid magenta] {\frac{1}{3}} \end{split} \end{equation*}

Contoh 04

\begin{equation*} \begin{split} & ^{25}\log \frac{1}{625} \\\\ & ^{\large{5^2}}\log 5^{-4} \\\\ & \frac{-4}{2} \: .\: ^5 \log 5 \\\\ & \bbox[5px, border: 2px solid magenta] {-2} \end{split} \end{equation*}

##### SOAL LATIHAN

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