Solving the Equation: (1/16)^x + 5 = 8^2
In this article, we will solve the equation (1/16)^x + 5 = 8^2. This equation involves exponential functions and requires some algebraic manipulation to solve for x.
Step 1: Simplify the Equation
First, let's simplify the right-hand side of the equation:
8^2 = 64
So, the equation becomes:
(1/16)^x + 5 = 64
Step 2: Isolate the Exponential Term
Subtract 5 from both sides of the equation to isolate the exponential term:
(1/16)^x = 64 - 5 (1/16)^x = 59
Step 3: Take the Logarithm
Take the logarithm of both sides of the equation to eliminate the exponent:
x * log(1/16) = log(59)
Step 4: Simplify and Solve for x
Simplify the equation by evaluating the logarithm:
x * (-4) = log(59)
Divide both sides by -4 to solve for x:
x = -log(59)/4
Final Answer
x = -log(59)/4
Therefore, the value of x that satisfies the equation (1/16)^x + 5 = 8^2 is x = -log(59)/4.