Answer:
Solution:
(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 is option (c) -0.4
The value of x to the nearest tenth is -0.4
Given the following expressions
(0.2)x = 2 and log 2 = 0.3010
Taking log of both sides of (0.2)x = 2
log (0.2)x = log 2.
x log (0.2) = 0.3010,
x [log 2 - log 10] = 0.3010.
Note that log2 2 = 1
x [log 2 - 1] = 0.3010
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306
Hence the value of x to the nearest tenth is -0.4
Learn more on logarithm here: https://brainly.com/question/25710806
Answer is option (c) -0.4
