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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