(1/16)^x+5=8^2

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Jun 12, 2024

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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.