Question

65. Find h if 3(2h-1) = 27(-h+2) A) 7 G D) 0​

Answer 1

Answer:

  A)  7/5

Step-by-step explanation:

An exponential equation like this can be solved by using logarithms, or by rewriting the bases so they are the same.

  3^(2h-1) = 27^(-h+2)

Using 27 = 3^3, we can write the equation in terms of powers of 3:

  3^(2h-1) = (3^3)^(-h+2)

  3^(2h -1) = 3^(-3h +6)

Equating exponents gives ...

  2h -1 = -3h +6

  5h = 7 . . . . . . . . . add 1+3h

  h = 7/5 . . . . . . . divide by 5

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Additional comment

When solving this using a graphing calculator, it is often convenient to write the equation in such a way that the solution is an x-intercept. Here, we can do that by subtracting the right-side expression from both sides:

  3^(2h-1) -27^(-h+2) = 0

The solution is h = 1.4 = 7/5.