Jika maka berada di antara ....

Pertanyaan

Jika $begin mathsize 14px style 2 to the power of 3 x plus 2 end exponent equals 48 end style$ maka $begin mathsize 14px style x end style$ berada di antara ....

$begin mathsize 14px style 1 space dan space 4 over 3 end style$
$begin mathsize 14px style 1 half space dan space 4 over 3 end style$
$size 14px 1 over size 14px 2 size 14px space size 14px dan size 14px space size 14px 1$
$size 14px minus size 14px 1 size 14px space size 14px dan size 14px space size 14px 4 over size 14px 3$
$size 14px 1 over size 14px 2 size 14px space size 14px dan size 14px space size 14px 4 over size 14px 3$

Pembahasan Soal:

Gunakan konsep logaritma berkut:

$begin mathsize 14px style a to the power of c equals b rightwards arrow log presuperscript a space b equals c log presuperscript a space b plus log presuperscript a space c equals log presuperscript a space open parentheses b c close parentheses end style$

Perhatikan perhitungan berikut untuk menentukan $begin mathsize 14px style x end style$ :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell 2 to the power of 3 x plus 2 end exponent end cell equals 48 row cell log presuperscript 2 space 48 end cell equals cell 3 x plus 2 end cell row cell 3 x plus 2 end cell equals cell log presuperscript 2 space 48 end cell row cell 3 x end cell equals cell log presuperscript 2 space 48 minus 2 end cell row cell 3 x end cell equals cell log presuperscript 2 space open parentheses 16 cross times 3 close parentheses minus 2 end cell row cell 3 x end cell equals cell log presuperscript 2 space 16 plus log presuperscript 2 space 3 minus 2 end cell row cell 3 x end cell equals cell log presuperscript 2 space 2 to the power of 4 plus log presuperscript 2 space 3 minus 2 end cell row cell 3 x end cell equals cell 4 minus 2 plus log presuperscript 2 space 3 end cell row cell 3 x end cell equals cell 2 plus log presuperscript 2 space 3 end cell row x equals cell fraction numerator 2 plus log presuperscript 2 space 3 over denominator 3 end fraction end cell row x equals cell fraction numerator 2 plus 1 comma 585 over denominator 3 end fraction end cell row x equals cell fraction numerator 3 comma 585 over denominator 3 end fraction end cell row x equals cell 1 comma 195 end cell end table end style$

Diperoleh nilai $begin mathsize 14px style x equals 1 comma 195 end style$ , artinya berada di antara $begin mathsize 14px style 1 space dan space 4 over 3 end style$ .

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021