Diketahui sin(x)=tan(x) dan P(x)=∣2 cos x∣. Tentukan nilai 28​log(P(x)⋅P(x)​).

Pertanyaan

Diketahui  dan . Tentukan nilai 

  1. ...  

  2. ... 

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari  begin mathsize 14px style scriptbase bold l bold o bold g begin bold style left parenthesis P left parenthesis x right parenthesis square root of P left parenthesis x right parenthesis end root right parenthesis end style end scriptbase presuperscript bold 2 square root of bold 8 end presuperscript end style adalah begin mathsize 14px style bold 3 over bold 5 end style 

Pembahasan

Pembahasan

Ingat!

begin mathsize 14px style tan open parentheses x close parentheses equals fraction numerator sin open parentheses x close parentheses over denominator cos open parentheses x close parentheses end fraction end style 

begin mathsize 14px style scriptbase log open parentheses b to the power of n close parentheses equals n over m scriptbase log open parentheses b close parentheses end scriptbase presuperscript a end scriptbase presuperscript a to the power of m end presuperscript scriptbase log open parentheses a close parentheses equals 1 space end scriptbase presuperscript a end style 

Karena begin mathsize 14px style sin open parentheses x close parentheses equals tan open parentheses x close parentheses end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin open parentheses x close parentheses end cell equals cell tan open parentheses x close parentheses end cell row cell sin open parentheses x close parentheses end cell equals cell fraction numerator sin open parentheses x close parentheses over denominator cos open parentheses x close parentheses end fraction end cell row cell cos open parentheses x close parentheses end cell equals 1 end table end style 

Sehingga

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis x right parenthesis end cell equals cell open vertical bar 2 cos open parentheses x close parentheses close vertical bar end cell row blank equals cell open vertical bar 2.1 close vertical bar end cell row blank equals cell open vertical bar 2 close vertical bar end cell row blank equals 2 end table end style 

Nilai dari 

  begin mathsize 14px style scriptbase log open parentheses P open parentheses x close parentheses square root of P open parentheses x close parentheses end root close parentheses space end scriptbase presuperscript 2 square root of 8 end presuperscript equals scriptbase log open parentheses 2 square root of 2 close parentheses end scriptbase presuperscript 2 to the power of 5 over 2 end exponent end presuperscript equals scriptbase log open parentheses 2 to the power of 3 over 2 end exponent close parentheses end scriptbase presuperscript 2 to the power of 5 over 2 end exponent end presuperscript equals open parentheses 3 over 2 divided by 5 over 2 close parentheses scriptbase log open parentheses 2 close parentheses end scriptbase presuperscript 2 equals open parentheses 3 over 5 close parentheses times 1 equals 3 over 5 end style 

Jadi, nilai dari  begin mathsize 14px style scriptbase bold l bold o bold g begin bold style left parenthesis P left parenthesis x right parenthesis square root of P left parenthesis x right parenthesis end root right parenthesis end style end scriptbase presuperscript bold 2 square root of bold 8 end presuperscript end style adalah begin mathsize 14px style bold 3 over bold 5 end style 

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Diketahui fungsi f(x)=ax+b.  Jika f(−2)=−5 dan f(2)=3, tentukan: a. Nilai a dan b  b. Rumus fungsi f(x)  c. Nilai f(5) dan f(9)  d. Nilai k sehingga f(k)=7

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