Solve log x² + 2*log 30 = 4*log 3 + 2*log 5 +log 100 for x.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation log x^2 + 2*log 30 = 4*log 3 + 2*log 5 +log 100  has to be solved.

log x^2 + 2*log 30 = 4*log 3 + 2*log 5 +log 100

=> log x^2 = 4*log 3 + 2*log 5 +log 100 - 2*log 30

Use the property of logarithm log a + log b = log(a*b), log a - log b = log(a/b) and a*log b = log b^a

=> log x^2 = log((3^4*5^2*100)/(30^2))

=> log x^2 = log(3^2*5^2)

=> x^2 = 3^2*5^2

=> x = -3*5 = -15 and x = 3*5 = 15

The solution of the equation is x = 15 and x = -15

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