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数学 高校生

172.3 これでも大丈夫ですか??

さい。 去。 ろえ -) g53 基本例題112 対数の表現 (1) 10g23=a, log35=6のとき, log210と1015 40 を a b で表せ。 1 logx b= log.xc= のとき, 10gabcxの値を求めよ。 8' 24 ga=1 (2) 10gxa= 1 3' (3) a,b,c を1でない正の数とし, 10gab=a, log.c=β, logca=y とする。 1 1 このとき, ab+By+ya=-+ + が成り立つことを証明せよ。 a B 指針 (1) 10,15, 40 をそれぞれ 分解して, 2, 3,5の積で表すことを考える。 (2) 10gabcx= logx abc (3) 右辺を通分すると, 分母に aβy が現れる。 これを計算してみる。 363510 1 また 解答 The Parent (1) log2 10=log2 (2-5) = log₂2+log25=1+log25 ここで よって log2 10 log₂ (2.5)=1+log₂5 底の変換公式を利用して, 10g25 をa, b で表す。 また 10g 15 40 は, 真数 40=5・2° に着目して,2を底とする対数で表す。 である。 10gxabcの値を求める。 1 log35 log32 log210=1+ab |_log25= log1540= == + 1/3 + a = r -= log₂3.log35=ab RETS S00 log2 40 log215 (2) ab+3 ab+3 a+ab a(b+1) = (2) logxabc=logxa+logxb+logxc= よって logabc X= 1 aβ+βy+ya...... ① aby log2 (5.2³) log2 (3.5) 1 logxabc a log25+3 Puiglog23+10g25 =2 aby=loga blogb clogca=logab. 1+1+1/0 であるから、①より したがって,等式は証明された。 1 1 1 + + 3 11 24 8 10gac.. loga blogac 1 2 cal =1 00000 [名城大] =aβ+βy+ya が成り立つ。 aduto 1 log32= log23 前ページ検討も参照。 ( 10g25 = ab (前半から) log■ [久留米大] (3) 別解 基本171 したがって (左辺) log 1 aβ=logablog.c=logac 同様に βy=10gba Ya=logcb =logac+loga+logcb 1 1 + + Y a B 練習 (1) 10g2=a, logs4=6とするとき, log158 をa, bを用いて表せ。 ③172 でない正の数とし, A=logza, Blog2 bとする。 a, bが 2=-1、ab=1を満たすとき, A, B の値を求めよ。 芝浦工大 (2)類 京都産大] (p.272 EX110 269 5章 30 対数とその性質

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英語 高校生

大学受験の長文問題です。 解答がないので答えをお願いします🙏

問題 3 以下の英文を読んで、次の問いに答えなさい。 (*のついた語には語注が ある。) If you are able to step outside and hear many types of birds, you might also have a greater feeling of well-being. Two studies show that hearing diverse birdsongs may help increase our happiness. (A) One study was done by researchers at California Polytechnic State University. A research team studied the effects of birdsong ( 1 ) people walking through a park in the U.S. state of Colorado. A biology graduate student, Danielle Ferraro, led the study. "There could be an evolutionary reason why we like birdsong so much. And the idea is that when we hear birdsong it could signal safety to us," Ferraro says. There could be many other reasons, too. Ferraro states that in some areas around the world birdsong can also signal the arrival of spring and nice weather. Bird diversity, she adds, can also mean a healthy environment. She explained her study to Voice of America (VOA). Ferraro and her team played recorded songs from a diverse group of birds native to the area. They did this on hiking trails in a park in Boulder, Colorado. (2) several weeks, the researchers played recorded birdsong at certain times of the day and other times they did not. Then they talked with hikers after they ( 3 ). Hikers who heard the recorded diverse birdsongs reported a greater sense of well-being than the people who heard simply the natural birds. The researchers suggest that both the bird sounds and biodiversity* can increase feelings of well-being. Ferraro explained that she used native birdsong for the study. This way it would sound as natural as possible. They also did the study during the summer. She explains why this is important. "So the study ( 4 ) in the summer and that's kind of important because the spring is most birds' breeding* season. And if we play the birdsong during breeding season, that might have disturbed them. (B) We didn't want to disturb the birds too much." The study was published in an academic journal called the Royal Society B in December 2020. - 10- ◇M2 (310-15)

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