`3^(x^2) = 7^(6 - x)` Solve the exponential equation algebraically. Approximate the result to three decimal places.

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kspcr111 | In Training Educator

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Given

`3^(x^2) = 7^(6 - x)`

applying logarithmicsĀ  on both sides we get

`ln(3^(x^2))=ln(7^(6 - x))`

=> `x^2 ln(3) = (6-x)ln(7)`

=> `x^2 ln(3) = 6*ln(7) - x* ln(7)`

=> `x^2 ln(3)+x* ln(7)-6*ln(7) =0`

=>on solving we get the value of x as

=> x = `(+- sqrt(ln(7) (24ln(3)+ln(7))) - ln(7))/(ln(9))`

=> `x= 2.4925 or x= -4.2637`