作业帮高一数学（对数和三角比）
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/09 19:48:29
高一数学（对数和三角比）
1.a>0,b>0,且aˆb=b^a,b=9a,则a=
2.log18(9)=a,18^b=5,则log36(45)=
3.解方程3^2x+3^3x=10*3^(x+2)
4.解方程log2(4^x+4)=x+log2(2^(x+1)-3)
5.化简1-sin(π+2α)+cos(2α-7π)/(1+cos(π-2α)+sin(2α+6π))
2楼的 我不懂为什么9alna=a(ln9+lna)
能化为9alna=aln9
再补充一道 已知锐角α终边上一点P（x,跟号5），则α等于（）
3 -3 3-π/2 π/2-3
第五题我已经做出来了 麻烦各位大大帮我做下其余的 我有追分啊
1.a>0,b>0,且aˆb=b^a,b=9a,则a=
2.log18(9)=a,18^b=5,则log36(45)=
3.解方程3^2x+3^3x=10*3^(x+2)
4.解方程log2(4^x+4)=x+log2(2^(x+1)-3)
5.化简1-sin(π+2α)+cos(2α-7π)/(1+cos(π-2α)+sin(2α+6π))
2楼的 我不懂为什么9alna=a(ln9+lna)
能化为9alna=aln9
再补充一道 已知锐角α终边上一点P（x,跟号5），则α等于（）
3 -3 3-π/2 π/2-3
第五题我已经做出来了 麻烦各位大大帮我做下其余的 我有追分啊
1,
b = 9a > 0,
a^b = b^a,blna = alnb,
9alna = alnb,
9lna = ln(a^9) = lnb,
9a = b = a^9,
9 = a^8,
a = 9^(1/8) = 3^(1/4)
2,
log18(9)=a,18^b=5,则log36(45)=
a = ln9/ln18 = 2ln3/[ln2 + 2ln3] = 1/[ln2/(2ln3) + 1],
ln2/(2ln3) + 1 = 1/a,
ln2/ln3 = 2(1/a -1) = 2(1-a)/a
bln18 = ln5,b = ln5/[ln2 + 2ln3] = [ln5/ln3]/[ln2/ln3 + 2],
ln5/ln3 = b[ln2/ln3 + 2] = b[2(1-a)/a + 2] = 2b/a
log36(45) = ln45/ln36 = [ln5 + 2ln3]/[2ln2 + 2ln3]
= [ln5/ln3 + 2]/[2ln2/ln3 + 2]
= [2b/a + 2]/[4(1-a)/a + 2]
= [b + a]/[2(1-a) + a]
= [b+a]/[2-a]
3,
3^(2x) + 3^(3x) = 10*3^(x+2),
3^x + 3^(2x) = 10*3^2,
0 = (3^x)^2 + (3^x) - 9*10 = [3^x + 10][3^x - 9],
3^x = 9,
x = 2.
4,
log2(4^x+4)=x+log2(2^(x+1)-3) = log2(2^x) + log2[2^(x+1) - 3]
= log2[2^(2x+1) - 3*2^x],
4^x + 4 = 2^(2x + 1) - 3*2^x = 2*4^x - 3*2^x,
0 = 4^x - 3*2^x - 4 = (2^x)^2 - 3*2^x - 4 = [2^x - 4][2^x + 1],
2^x = 4,
x = 2.
5,
(略)
【补充】
已知锐角α终边上一点P（x,跟号5）,则α等于（）
A.3 B.-3 C.3-π/2 D.π/2-3
锐角α,0 < α < π/2.
3 > π/2,A错.
-3 < 0,B错.
0 < 3 - π/2 < π - π/2 = π/2,符合要求.
π/2 - 3 < 0,D错.
所以,选C.
b = 9a > 0,
a^b = b^a,blna = alnb,
9alna = alnb,
9lna = ln(a^9) = lnb,
9a = b = a^9,
9 = a^8,
a = 9^(1/8) = 3^(1/4)
2,
log18(9)=a,18^b=5,则log36(45)=
a = ln9/ln18 = 2ln3/[ln2 + 2ln3] = 1/[ln2/(2ln3) + 1],
ln2/(2ln3) + 1 = 1/a,
ln2/ln3 = 2(1/a -1) = 2(1-a)/a
bln18 = ln5,b = ln5/[ln2 + 2ln3] = [ln5/ln3]/[ln2/ln3 + 2],
ln5/ln3 = b[ln2/ln3 + 2] = b[2(1-a)/a + 2] = 2b/a
log36(45) = ln45/ln36 = [ln5 + 2ln3]/[2ln2 + 2ln3]
= [ln5/ln3 + 2]/[2ln2/ln3 + 2]
= [2b/a + 2]/[4(1-a)/a + 2]
= [b + a]/[2(1-a) + a]
= [b+a]/[2-a]
3,
3^(2x) + 3^(3x) = 10*3^(x+2),
3^x + 3^(2x) = 10*3^2,
0 = (3^x)^2 + (3^x) - 9*10 = [3^x + 10][3^x - 9],
3^x = 9,
x = 2.
4,
log2(4^x+4)=x+log2(2^(x+1)-3) = log2(2^x) + log2[2^(x+1) - 3]
= log2[2^(2x+1) - 3*2^x],
4^x + 4 = 2^(2x + 1) - 3*2^x = 2*4^x - 3*2^x,
0 = 4^x - 3*2^x - 4 = (2^x)^2 - 3*2^x - 4 = [2^x - 4][2^x + 1],
2^x = 4,
x = 2.
5,
(略)
【补充】
已知锐角α终边上一点P（x,跟号5）,则α等于（）
A.3 B.-3 C.3-π/2 D.π/2-3
锐角α,0 < α < π/2.
3 > π/2,A错.
-3 < 0,B错.
0 < 3 - π/2 < π - π/2 = π/2,符合要求.
π/2 - 3 < 0,D错.
所以,选C.