%5Ex-9%3D4.jpeg "(1/16)^x-9=4")
Solving the Equation (1/16)^x - 9 = 4
In this article, we will solve the equation (1/16)^x - 9 = 4 and find the value of x.
Rewriting the Equation
First, let's rewrite the equation by adding 9 to both sides:
(1/16)^x = 4 + 9
(1/16)^x = 13
Taking the Logarithm
To solve for x, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln):
ln((1/16)^x) = ln(13)
Using the property of logarithms, we can rewrite the left side of the equation as:
x * ln(1/16) = ln(13)
Simplifying the Equation
Now, let's simplify the equation by evaluating the logarithm of 1/16:
x * (-ln(16)) = ln(13)
x * (-4*ln(2)) = ln(13)
Solving for x
Now, let's solve for x:
x = ln(13) / (-4*ln(2))
x ≈ 2.35
Therefore, the value of x is approximately 2.35.
Conclusion
In this article, we solved the equation (1/16)^x - 9 = 4 and found that the value of x is approximately 2.35.
