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log2为底256的对数

答案为3

log8 256= log2 256 / log2 8= 8log2 2 / 3log2 2= 8/3

log2 5 = x (1)2^x = 5 (2)对 一般计算器和数学用表没有以2为底的对数计算或表可用,这时用换底公式:对(2)两边取10进对数,log 2^x = x log 2 = log 5 x = log 5 / log 2 ≈ 2.3219

2^2=42^3=82^4=162^5=322^6=64X=log(2)(64)X=6

由题可知:2^x<=256,所以x<=8 log2(x)>=0.5,所以x>= 根号2所以根号2<=x<=8【log根号2(根号x/2)=[ (1/2)/(1/2) ] log2(X/2)=log2(X/2)f(x)= [ log2(X/2) ]所以,当x=2时,f(x)最小,f(2)=0;当x=8时,f(x)最大,f(8)=9.

log2 3*log8 4=log2 3*(2/3)log2 2=(2/3)log2 3=(2/3)lg3/lg2

解答:(1)2^x≤256即2^x≤2^8∴ x≤8(2)log2(x)≥1/2即log2(x)≥log2 (√2)∴ x≥√2∴ √2≤x≤8f(x)=log2(x/2)*log√2 (√x/2) =log2(x/2)*log2(x/4) =[log2(x)-1]*[log2(x)-2]令log2(x)=t,则1/2≤t≤3∴ f(x)=(t-1)(t-2) =t-3t+2 =(t-3/2)-1/4∴ t=3/2时,f(x)有最小值-1/4当t=3时,f(x)有最大值2

根据换底公式:log2为底9的对数=log3为底9的对数除以log3为底2的对数log3为底2的对数=log3为底2的对数除以log3为底3的对数两者相乘,约分后得 log3为底9的对数除以log3为底3的对数=3

log以2为底7的对数=lg7/lg2=2.8073549220576041074419693172318

Log eight of two

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