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Gold in the Exponent (Posted on 2019-12-11)

What real value of x satisfies the equation 9^x + 12^x = 16^x?

See The Solution Submitted by Brian Smith

Rating: 4.0000 (1 votes)

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solution--our phamous phriend

| Comment 2 of 6 |

Divide by 12^x and set a = (4/3)^x to get 1/a + 1 = a.

Solution indeed gives phi: a=(1+sqrt(5))/2 so that

x=(log a)/((log 4) - (log 3))

=1.6727209344623325445854312524198 to the limits of Mr. Gates' calculator and in agreement with Charlie's solution.

Posted by xdog on 2019-12-11 14:44:27

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