Question

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

(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0

Answer 1

Solutions


(0.2)x = 2.

Taking log on both sides 

log (0.2)x = log 2.

x log (0.2) = 0.3010, [since log 2 = 0.3010].

x log (2/10) = 0.3010.

x [log 2 - log 10] = 0.3010.

x [log 2 - 1] = 0.3010,[since log 10=1].

x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].

x[-0.699] = 0.3010.

x = 0.3010/-0.699.

x = -0.4306….

x = -0.4 (nearest tenth)

Answer: (c)

Answer 2

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

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