log4 sin(3π)/4+log9 tan[(-5π)/6]=_______.
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log4 sin(3π)/4+log9 tan[(-5π)/6]=_______.
log4 sin(3π)/4+log9 tan[(-5π)/6]
=log4 sin(π)/4+log9 tan[2π+(-5π)/6]
=log4 (√2/2)+log9 tan[7π/6]
=log4 (2^(1/2))+log9 √3
=log4 (4^(1/4))+log9 9^(1/4)
=1/4+1/4
=1/2
再问: √2/2怎么是化成2^(1/2)?2^(1/2)不是√2吗?
再答: 你说得对log4 sin(3π)/4+log9 tan[(-5π)/6] =log4 sin(π)/4+log9 tan[2π+(-5π)/6] =log4 (√2/2)+log9 tan[7π/6] =log4 (2^(-1/2))+log9 √3 =log4 (4^(-1/4))+log9 9^(1/4) =-1/4+1/4 =0
再问: 不是应该tan(7π/6)=tan30°=√3/3么
再答: 怎么做题,不细心,不好意思 log4 sin(3π)/4+log9 tan[(-5π)/6] =log4 sin(π)/4+log9 tan[2π+(-5π)/6] =log4 (√2/2)+log9 tan[7π/6] =log4 (2^(-1/2))+log9 (√3/3) =log4 (4^(-1/4))+log9 9^(-1/4) =-1/4-1/4 =-1/2
=log4 sin(π)/4+log9 tan[2π+(-5π)/6]
=log4 (√2/2)+log9 tan[7π/6]
=log4 (2^(1/2))+log9 √3
=log4 (4^(1/4))+log9 9^(1/4)
=1/4+1/4
=1/2
再问: √2/2怎么是化成2^(1/2)?2^(1/2)不是√2吗?
再答: 你说得对log4 sin(3π)/4+log9 tan[(-5π)/6] =log4 sin(π)/4+log9 tan[2π+(-5π)/6] =log4 (√2/2)+log9 tan[7π/6] =log4 (2^(-1/2))+log9 √3 =log4 (4^(-1/4))+log9 9^(1/4) =-1/4+1/4 =0
再问: 不是应该tan(7π/6)=tan30°=√3/3么
再答: 怎么做题,不细心,不好意思 log4 sin(3π)/4+log9 tan[(-5π)/6] =log4 sin(π)/4+log9 tan[2π+(-5π)/6] =log4 (√2/2)+log9 tan[7π/6] =log4 (2^(-1/2))+log9 (√3/3) =log4 (4^(-1/4))+log9 9^(-1/4) =-1/4-1/4 =-1/2
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