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Câu hỏi: Nếu $lo{{g}_{2}}x=5lo{{g}_{2}}a+4lo{{g}_{2}}b\left( a>0, b>0 \right)$ thì giá trị xbằng:
A. ${{a}^{4}}{{b}^{5}}$
B. ${{a}^{5}}{{b}^{4}}$
C. ${{a}^{5}}+{{b}^{4}}$
D. ${{a}^{4}}+{{b}^{5}}$
A. ${{a}^{4}}{{b}^{5}}$
B. ${{a}^{5}}{{b}^{4}}$
C. ${{a}^{5}}+{{b}^{4}}$
D. ${{a}^{4}}+{{b}^{5}}$
Phương pháp:
Sử dụng công thức $lo{{g}_{a}}~x~=mlog{{~}_{a}}x,log{{~}_{a}}x+log{{~}_{a}}y=lo{{g}_{a}}\left( xy \right)\left( 0<a\ne 1,x,y>0 \right).~$
${{\log }_{2}}x=5{{\log }_{2}}a+4{{\log }_{2}}b\left( a>0,b>0 \right)$
$\Leftrightarrow {{\log }_{2}}x={{\log }_{2}}{{a}^{5}}+{{\log }_{2}}{{b}^{4}}$
$\Leftrightarrow {{\log }_{2}}x={{\log }_{2}}\left( {{a}^{5}}{{b}^{4}} \right)$
$\Leftrightarrow x={{a}^{5}}{{b}^{4}}$
Sử dụng công thức $lo{{g}_{a}}~x~=mlog{{~}_{a}}x,log{{~}_{a}}x+log{{~}_{a}}y=lo{{g}_{a}}\left( xy \right)\left( 0<a\ne 1,x,y>0 \right).~$
${{\log }_{2}}x=5{{\log }_{2}}a+4{{\log }_{2}}b\left( a>0,b>0 \right)$
$\Leftrightarrow {{\log }_{2}}x={{\log }_{2}}{{a}^{5}}+{{\log }_{2}}{{b}^{4}}$
$\Leftrightarrow {{\log }_{2}}x={{\log }_{2}}\left( {{a}^{5}}{{b}^{4}} \right)$
$\Leftrightarrow x={{a}^{5}}{{b}^{4}}$
Đáp án B.