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atroni [7]
2 years ago
12

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

Mathematics
2 answers:
prisoha [69]2 years ago
7 0

<em><u>(0.2)x = 2.</u></em>

<em><u>Taking log on both sides</u></em>

<em><u>log (0.2)x = log 2.</u></em>

<em><u>x</u></em><em><u> </u></em><em><u>log (0.2) = 0.3010, [since log 2 = 0.3010].</u></em>

<em><u>x</u></em><em><u> </u></em><em><u>log (2/10) = 0.3010.</u></em>

<em><u>x</u></em><em><u> </u></em><em><u>[log 2 - log 10] = 0.3010.</u></em>

<em><u>x</u></em><em><u> </u></em><em><u>[log 2 - 1] = 0.3010,[since log 10=1].</u></em>

<em><u>x[-0.699] = 0.3010.</u></em>

<em><u>x</u></em><em><u>=</u></em><em><u> </u></em><em><u>0.3010/-0.699.</u></em>

<em><u>x</u></em><em><u>=</u></em><em><u> </u></em><em><u>= -0.4306….</u></em>

<em><u>x</u></em><em><u>=</u></em><em><u> </u></em><em><u>= -0.4</u></em><em><u>.</u></em>

yawa3891 [41]2 years ago
7 0

<em><u>(0.2)x = 2.</u></em>

<em><u>Taking log on both sides</u></em>

<em><u>log (0.2)x = log 2.</u></em>

<em><u>x log (0.2) = 0.3010, [since log 2 = 0.3010].</u></em>

<em><u>x log (2/10) = 0.3010.</u></em>

<em><u>x</u></em><em><u> </u></em><em><u>[log 2 - log 10] = 0.3010.</u></em>

<em><u>x [log 2 - 1] = 0.3010,[since log 10=1].</u></em>

<em><u>x[-0.699] = 0.3010.</u></em>

<em><u>x = 0.3010/-0.699</u></em>

<em><u>x</u></em><em><u> </u></em><em><u>=</u></em><em><u> </u></em><em><u>-0.4306</u></em>

<em><u>x</u></em><em><u>= -0.4 (nearest tenth)</u></em>

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