Solve for the input: r(x) = 3 ln(1.2)(1.2^x); r(x) = 9.7, r(x) = 20

Question

Solve for the input that corresponds to the given output value. (Round answers to three decimal places when appropriate. Enter your answers as a comma-separated list. Note: Even though the question may be completed without the use of technology, the authors intend for you to complete the activity using the technology you will be using in the remainder of the course so that you become familiar with the basic functions of that technology.)

Answer 1

r(x) = 9.7

3ln(1.2)(1.2^x) = 9.7

Note that the answer we'll get is highly dependent on the question being worded correctly.  For example, ln(1.2)(1.2^x) is not the same thing as ln( (1.2)(1.2^x) ).

1.2^x = 9.7/(3ln(1.2))

ln(1.2^x) = ln( 9.7/(3ln(1.2)) )

xln(1.2) = ln( 9.7/(3ln(1.2)) )

x = ln( 9.7/(3ln(1.2)) ) / ln(1.2)

x = about 15.772

.

r(x) = 20

x = ln( 20/(3ln(1.2)) ) / ln(1.2)

x = about 19.740