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94.59=4.9303ln(x)+69.093

 Sep 12, 2016
 #1
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Solve for x:
94.59 = 69.093+4.9303 log(x)

94.59 = 9459/100 and 69.093+4.9303 log(x) = 69093/1000+(49303 log(x))/10000:
9459/100 = 69093/1000+(49303 log(x))/10000

9459/100 = 69093/1000+(49303 log(x))/10000 is equivalent to 69093/1000+(49303 log(x))/10000 = 9459/100:
69093/1000+(49303 log(x))/10000 = 9459/100

Subtract 69093/1000 from both sides:
(49303 log(x))/10000 = 25497/1000

Multiply both sides by 10000/49303:
log(x) = 254970/49303

Cancel logarithms by taking exp of both sides:
Answer: |x = e^(254970/49303)

 Sep 12, 2016
 #2
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Subtract 69.093 from both sides

 

4.9303ln(x) = (94.59-69.093)

 

Divide both sides by 4.9303

 

ln(x) = (94.59-69.093)/4.9303 ≈ 5.17149

 

Exponentiate both sides

 

x  = e^5.17149 ≈ 176.2

 Sep 12, 2016

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