Question

f(x) = 20(1.5)x. Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.

Answer 1

Answer:

$x=log_{1.5}(\frac{y}{20})$

Step-by-step explanation:

Considering the function:

$f(x) = 20\, (1.5)^x$

The independent variable is "x" and we are asked to model it in terms of the variable "y":

$f(x) = 20\, (1.5)^x\\y=20\, (1.5)^x$

Then, in order to solve for x (which resides in the exponent), we need to use the logarithm function.

Since the base of the exponent is 1.5, we need to use the logarithm base 1.5, to lower that exponent "x":

$y=20\, (1.5)^x\\\frac{y}{20} =(1.5)^x\\log_{1.5}(\frac{y}{20}) =x\\x=log_{1.5}(\frac{y}{20})$