Given that 10\(^x\) = 0.2 and log\(_{10}\)2 = 0.3010, find x
A
-1.3010
B
-0.6990
C
0.6990
D
1.3010
E
0.02
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Given that log\(_{10}\)2 = 0.3010, If 10\(^x\) = 0.2
log\(_{10}\)10\(^x\) = log\(_{10}\) 0.2 = x = log\(_{10}\)0.2
But 0.2 = 2 x 10\(^{-1}\), so log\(_{10}\)0.2 = log\(_{10}(2 \times 10^{-1})\), x = log\(_{10}\)2 + log\(_{10}\)10\(^{-1}\)
x = 0.3010 - 1
x = - 0.6990
Source: Myschool Past Questions Archive (Record #32586)