Question

If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
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Answer 1

0.2 x=2

x= 2/0.2= 10,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

ALTERNATE METHOD (CONSIDERING A DIFFERENT FORMAT OF QUESTION)

Considering the question to be

0.2 ^ x= 2

Taking log of both sides,

x log0.2= log 2

x=log2/log0.2=log2/log(2/10)=log2/log2-log10

x= log 2/log 2-1= 0.301/-0.699=-30/70= -3/7 (approx)= -0.4

Answer 2

$\huge{\mathfrak{Solution:}}$



$\sf (0.2)x = 2. \\ \\ \sf Taking \: log \: on \: both \: sides , \\ \\ \therefore \sf\log (0.2)x = \log 2. \\ \to \sf x \log (0.2) = 0.3010\: \: \: [since \: \log 2 = 0.3010]\\ \to \sf x \log \bigg( \frac{2}{10} \bigg) = 0.3010 \\ \sf\to x [ \log 2 - \log 10] = 0.3010 \\ \sf\to x [ \log 2 - 1] = 0.3010 \: \: \: \: \: \: \: \: \: [since \log \: 10=1]. \\ \to \sf x [0.3010 -1] = 0.3010, \: \: \: \: \: \: \: \: [since \log 2 = 0.3010]. \\ \sf\to x[-0.699] = 0.3010. \\ \sf \to x = \frac{0.3010}{-0.699} \\ \sf\to x = -0.4306…. \\ \sf \to x = -0.4 \: \: \: (N earest \: Tenth)$