Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

2 ^ x = 3 ^ (x + 1) solve for x

Sagot :

sqdancefan

Answer:

  -2.71

Step-by-step explanation:

This exponential equation can be solved by rewriting it so there is only one base, then using logarithms.

__

solve for x

  2^x = 3^(x+1) . . . . . given

  2^x = 3·3^x . . . . . . eliminate the constant in the exponent

  (2/3)^x = 3 . . . . . . . divide by 3^x

  x·log(2/3) = log(3) . . . . take logarithms

  x = log(3)/log(2/3) ≈ -2.7095113

The value of x is about -2.71.

__

Alternate solution

Taking logarithms transforms this exponential equation to a linear equation.

  x·log(2) = (x +1)·log(3) . . . . take logs

  x(log(2) -log(3)) = log(3) . . . . . . subtract x·log(3)

  x = log(3)/(log(2) -log(3)) = log(3)/log(2/3) . . . . . same result as above

_____

Additional comment

In the attached, we have used a graphing calculator to find the x-intercept of the function f(x) = 0, where f(x) = 2^x -3^(x+1). This is the solution to the given equation.

The applicable rules of logarithms are ...

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

View image sqdancefan
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.