The solution to the exponential equation 172(2)x=272 can be found without the use of an over/under table as the solution is an integer value. Find the solution.
11
8
11.17
5
To solve the exponential equation 172(2)x = 272, we need to simplify the equation.
First, divide both sides of the equation by 172:
(2)x = 272/172
Simplify the right side:
(2)x = 1.5814...
To find the value of x, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm:
ln((2)x) = ln(1.5814...)
Using the property of logarithms, we can bring down the exponent:
x ln(2) = ln(1.5814...)
Divide both sides of the equation by ln(2):
x = ln(1.5814...)/ln(2)
Using a calculator, we find:
x ≈ 0.7507...
Since the solution is not an integer value, the answer is not one of the given options.