Question

Any expert plz... solve full solution


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

0.2x = 2

log 0.2x = log 2

x log 0.2 = 0.301

x = 0.301/log 0.2

x = -0.43063364398

 

To the nearest tenth, x = -0.4

Answer 2

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(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)

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