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If `(0.2)^x = 2` and `log_10 2 = 0·3010,` then what is the value of `x` to the nearest tenth ?

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If `(0.2)^x = 2` and `log_10 2 = 0·3010,` then what is the value of `x` to the nearest tenth ?
A. `-10.0`
B. `-0.5`
C. `-0.4`
D. `-0.2`
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Correct Answer - C
`(0.2)^(x)=2`
Taking log on both sides,
`xlog_(10).(2)/(10)=log_(10)2`
`x[log_(10)2-log_(10)10]=log_(10)2`
`x[0.3010-1]=0.3010`
`x=-(0.3010)/(0.6990)=-0.43`
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