ols
If x= Log y=Log 3
Express in terms of x and
y of (log to60 2
Answers
Step-by-step explanation:
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Given, x=log_2\,3\:\:and\:\:y=log_2\,5x=log23andy=log25
We use the following results,
log_e\,e=1logee=1
log\,a\times b=log\,a+log\,bloga×b=loga+logb
log\,\frac{a}{b}=log\,a-log\,blogba=loga−logb
log\,x^a=a.log\,xlogxa=a.logx
i).
log_2\,7.5=log_2\frac{75}{10}=log_2\,\frac{15}{2}=log_2\,15-log_2\,2log27.5=log21075=log2215=log215−log22
=log_2\,(3\times5)-1=log_2\,3+log_2\,5-1=x+y-1=log2(3×5)−1=log23+log25−1=x+y−1
ii).
log_2\,6750=log_2(5^3\times2\times3^3)=log_2\,5^3+log_2\,2+log_2\,3^3log26750=log2(53×2×33)=log253+log22+log233
=log_2\,5^3+1+log_2\,3^3=3.log_2\,5+1+3.log_2\,3=3y+1+3x=log253+1+log233=3.log25+1+3.log23=3y+1+3x
Therefore, log_2\,7.5=log_2\,3+log_2\,5-1=x+y-1log27.5=log23+log25−1=x+y−1 and log_2\,6750=3y+1+3xlog26750=3y+1+3x