標題:

10^(3log2)=?

發問:

ecaluate the following expressions without using calculator 10^(3log2)=? 100^log9 *100^(1/2log3)=?

最佳解答:

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10^(3log2) = (10^log2)^3 since the inverse function of 10^x is log x, 10^(log x) = log (10^x) = x = 2^3 = 8 100^log9 *100^(1/2log3) = (10^2)^log9 x (10^2)[(1/2) log 3] = (10^log9)^2 x (10^2)[log 3^(1/2)] = 9^2 x [10^(log3^(1/2))]^2 = 81 x [3^(1/2)]^2 = 81 x 3 = 243

其他解答:

10^(3log2)=y 3log2=logy log8=logy y=8 100^log9=x log9=logx x=9 100^(1/2log3)=y 1/2log3=logy log3^(1/2)=logy y=3^(1/2) 100^log9 *100^(1/2log3) =9*3^(1/2)
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