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

Answer:

c option is correct

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Explanation:

0.2)

x

=2⟹x=log

0.2

2=

log

2

0.2

1

=

1−log

2

10

1

=

1−

0.3010

1

1

[∵log2=0.3010]

∴x=−0.4

Answer 2

(0.2) x = 2

taking log on both sides

∴log(0.2)x = log (2)

⇛xlog (0.2) = 0.3010

⇛x log

$\frac{2}{10}$

= 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)