5^2x-1=27.6

solve for x

Thank you, Michelle

I think you mean

52x-1 = 27.6

Take natural logs of both sides:

ln(52x-1) = ln(27.6)

Now use the rule ln(MN) = N·ln(M) on the left side:

(2x - 1)ln(5) = ln(27.6)

Let A = ln(5) and B = ln(27.6)

(If you have a TI graphing calculator,
a good idea here would be to store these
two logs as A and B)

    (2x-1)A = B

    A(2x-1) = B

    2Ax - A = B

        2Ax = B + A

Divide both sides by 2A

          x = (B + A)/(2A)

Now replace A by ln(5) and B by ln(27.6)

  x = [ln(27.6) + ln(5)]/[2·ln(5)]

  x =  1.530737423

----------------------

Note: If the A and B above confuses you, 
then go back to this step:

             (2x - 1)ln(5) = ln(27.6)

find the logs on the calculator, and substitute:

     (2x - 1)(1.609437912) = 3.317815773

       1.609437912(2x - 1) = 3.317815773

3.218875825x - 1.609437912 = 3.317815773 

Add 1.609437912 to both sides:

              3.218875825x = 3.317815773 + 1.609437912 

              3.218875825x = 4.927253685

Divide both sides by coefficient 3.218875825

                         x = 4.927253685/3.218875825

                         x = 1.530737423

Edwin