Question

指数对数数学题已知10的α次方等于2的负二分之一次方,10的β次方等于32的三分之一次方.求 10的2α次方减四分之三β

Answer 1

10^a=2^(-1/2)

10^b=32^(1/3)

10^(2a-3/4b)

=10^2a/10^(3/4b)

=(10^a)^2/(10^b)^3/4

=(2^(-1/2))^2/[32^(1/3)]^3/4

=2^(-1)/32^1/4

=(1/2)/2^5/4

=(1/2)/2*2^(1/4)

=2^(-1-5/4)

=2^(-9/4)