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Solve this equation for x to the nearest tenth. `7^(4x-3) =20`

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rosey-girl | Student, Grade 12 | Valedictorian

Posted May 6, 2013 at 3:33 AM via web

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Solve this equation for x to the nearest tenth.

`7^(4x-3) =20`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 6, 2013 at 3:45 AM (Answer #1)

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The equation `7^(4x-3) = 20` has to be solved for x.

`7^(4x-3) = 20`

take the log of both the sides

`log(7^(4x - 3)) = log 20`

use the property `log a^b = b*log a`

=> `(4x - 3)*log 7 = log 20`

=> `4x - 3 = log 20/ log 7`

=> `x = (3 + log 20/ log 7)/4`

=> `x ~~ 1.13`

The solution of the equation is `x ~~ 1.1`

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