Pertanyaan

Nilai dari b b l o g l i m x → ∞ b 10 x n + bx b 1 x n − 10 bx dengan n > 1 adalah ....

Nilai dari $b^{_{b} l o g l i m_{x \to \infty} \frac{\frac{1}{b} x ^{n} - 10 bx}{\frac{10}{b} x ^{n} + bx}}$ dengan $n > 1$ adalah .... $\;$

N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa terdapat sifat logaritma sehingga kita dapatkan Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa terdapat sifat logaritma sehingga kita dapatkan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight b to the power of log presubscript blank presuperscript straight b invisible function application limit as straight x rightwards arrow straight infinity of invisible function application fraction numerator 1 over straight b straight x to the power of straight n minus 10 bx over denominator 10 over straight b straight x to the power of straight n plus bx end fraction end exponent end cell equals cell limit as straight x rightwards arrow straight infinity of invisible function application fraction numerator 1 over straight b straight x to the power of straight n minus 10 bx over denominator 10 over straight b straight x to the power of straight n plus bx end fraction end cell row blank equals cell limit as straight x rightwards arrow straight infinity of invisible function application fraction numerator open parentheses 1 over straight b minus fraction numerator 10 straight b over denominator straight x to the power of straight n minus 1 end exponent end fraction close parentheses straight x to the power of straight n over denominator open parentheses 10 over straight b plus b over straight x to the power of straight n minus 1 end exponent close parentheses straight x to the power of straight n end fraction end cell row blank equals cell limit as straight x rightwards arrow straight infinity of invisible function application fraction numerator 1 over straight b minus fraction numerator 10 straight b over denominator straight x to the power of straight n minus 1 end exponent end fraction over denominator 10 over straight b plus b over straight x to the power of straight n minus 1 end exponent end fraction semicolon space n greater than 1 end cell row blank equals cell fraction numerator 1 over straight b minus 0 over denominator 10 over straight b plus 0 end fraction end cell row blank equals cell fraction numerator 1 over straight b over denominator 10 over straight b end fraction end cell row blank equals cell 1 over straight b times straight b over 10 end cell row blank equals cell 1 over 10 end cell end table end style$

Jadi, jawaban yang tepat adalah C.