KembarnyAminRivalnyaEsKelapaMuda: Contoh Soal Matematika SMA dan Pembahasannya

Contoh Soal:

Harga x yang memenuhi $\sqrt{3^{2x+1}}=9^{x-2}$ adalah...
Nilai x yang memenuhi persamaan $\begin{matrix} _{}^{2}\textrm{log} & _{}^{3}\textrm{log} \end{matrix}\left ( 4^{2x-1}-7 \right )=1$ adalah...
Nilai x yang memenuhi $\begin{matrix} _{}^{x}\textrm{log} & \left ( _{}^{2}\textrm{log\, 8} \right ) \end{matrix}=2$ adalah...
Jika $\begin{matrix} _{}^{3}\textrm{log}\, 15\, =\, p\: \: \: dan\: & _{}^{5}\textrm{log}\, 4\, =\, 4 \end{matrix}\: \: \: maka\: \: \: _{}^{4}\textrm{log}\, 15\, =\: ...?$

Pembahasan:
1. $\sqrt{3^{2x+1}}=9^{x-2}$

$\left ( 3^{2x+1} \right )^{\frac{1}{2}}=3^{2(x-2)}$

$3^{x+\frac{1}{2}}=3^{2x-4}$

$x\, +\frac{1}{2}=2x-4$

$\frac{1}{2}\, +4=2x-x$

$\frac{9}{2}=x \rightarrow x=4\frac{1}{2}$

2. $\begin{matrix} _{}^{2}\textrm{log} & _{}^{3}\textrm{log} \left ( 4^{2x-1}-7 \right )\, =\, 1\end{matrix}$

$\begin{matrix} _{}^{3}\textrm{log} \left ( 4^{2x-1}-7 \right )\, =\, 2^{1}\end{matrix}$
   $4^{2x-1}-7\, =\, 3^{2}$
   $4^{2x-1}-7\, =\, 9 + 7$
   $4^{2x-1}-7\, =\, 16$
   $4^{2x-1}-7\, =\, 4^{2}$
$2x-1\, =\, 2$

$x\, =\, \frac{3}{2}$
3.    $\begin{matrix} _{}^{x}\textrm{log} & \left ( _{}^{2}\textrm{log\, 8} \right ) \end{matrix}\, =\, 2$
$\begin{matrix} _{}^{2}\textrm{log\, 8} \end{matrix}\, =\, x^{2}$
$_{}^{2}\textrm{log}\, 2^{3}\, =\, x^{2}$
   $3\, =\, x^{2}$
   $\left (3 \right )^{\frac{1}{2}}\, =\, \left (x^{2} \right )^{\frac{1}{2}}$
$x\, =\sqrt{3}$

Untuk mengerjakan no. 3 dan 4
Ingat!!! Sifat Logaritma: $_{}^{a}\textrm{log\, b\, =\, c}\, \rightarrow \, b\, =\, a^{c}$