Problem: If (0.2)x=2(0.2)^{x}=2(0.2)x=2 and log2=0.3010\log 2=0.3010log2=0.3010, then the value of xxx to the nearest tenth is:
Answer Choices:
A. −10-10−10
B. −0.5-0.5−0.5
C. −0.4-0.4−0.4
D. −0.2-0.2−0.2
E. 101010 Solution:
(210)x=2;∴log(210)x=xlog210=x(log2−log10)=log2\left(\dfrac{2}{10}\right)^{x}=2 ; \quad \therefore \log \left(\dfrac{2}{10}\right)^{x}=x \log \dfrac{2}{10}=x(\log 2-\log 10)=\log 2(102)x=2;∴log(102)x=xlog102=x(log2−log10)=log2.
∴x=0.30100.3010−1∼−0.4\therefore x=\dfrac{0.3010}{0.3010-1} \sim-0.4∴x=0.3010−10.3010∼−0.4.