Problem: If 10109=8x+510^{\log _{10} 9}=8 x+510log109=8x+5 then xxx equals:
Answer Choices:
A. 000
B. 12\dfrac{1}{2}21
C. 58\dfrac{5}{8}85
D. 98\dfrac{9}{8}89
E. 2103−58\dfrac{2 \log _{10} 3-5}{8}82log103−5 Solution:
Since 10109=8x+5,(109)(1010)=10(8x+5)∴9=8x+5∴x=1/210^{\log _{10} 9}=8 \mathrm{x}+5,\left(\log _{10} 9\right)\left(\log _{10} 10\right)=\log _{10}(8 x+5) \quad \therefore 9=8 \mathrm{x}+5 \quad \therefore \mathrm{x}=1 / 210log109=8x+5,(log109)(log1010)=log10(8x+5)∴9=8x+5∴x=1/2