Question

7. If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is?​

Answer 1

(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[-0.699] = 0.3010.

x = 0.3010/-0.699

x = -0.4306

x= -0.4 (nearest tenth)

Answer 2

(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[-0.699] = 0.3010.

x= 0.3010/-0.699.

x= = -0.4306….

x= = -0.4.