Question

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

Answer 1

★The equation

(0.2)^x   =   2

♡Apply logarithm to each side

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 [ - 0.699 ]   =   0.3010

x [ 0.3010 - 1 ]   =   0.3010

x    =   0.3010/ (-0.699}

x  =  - 0.430

x  =  - 0.4              [The value of 'x' to the nearest tenth]

hope it helps you!!

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 - -0.4


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