Question

Solve the linear equation: title="4^{2x+7} = 8^{2x-3}" alt="4^{2x+7} = 8^{2x-3}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

  x = 11.5

Step-by-step explanation:

Taking the logarithm base 2 will transform this to a linear equation.

  2(2x+7) = 3(2x -3)

  0 = 3(2x -3) -2(2x +7) . . . . subtract the left side

  0 = 2x -23 . . . . . . . . . . . . . simplify

  0 = x - 23/2 . . . . . . . . . . . . divide by 2

  11.5 = x . . . . . . . . . . . . . . . . add 11.5

The solution is x = 23/2 = 11.5.

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Check

This value of x makes the equation become ...

  4^(2·23/2 +7) = 8^(2·23/2 -3)

  4^30 = 8^20 . . . . . true