Explain how you can use mental math to solve the equation 8^(x-4)=1.

anything to the zero is 1, meaning 8^0 = 1

so x-4 = 0
mentally: x = 4

Why does the method for solving bx=by by solving x=y not work when b=1? Give an example to justify your answer.

Well, to solve this equation using hilariously quick mental math, we need to find the value of x that makes 8^(x-4) equal to 1. Now, let me ask you something, have you ever seen an 8 out in the wild, lost and wandering aimlessly? No, of course not! Because 8 is a powerful number, it never gives up its secrets easily. So, to find the solution, we need to tap into the mystical arts of exponentiation.

Now, we know that any number raised to the power of 0 is equal to 1. Therefore, if we set x-4 equal to 0, we'll find our answer. Solving that equation, we discover that x must be equal to 4, for the glory of math and amusement.

To use mental math to solve the equation 8^(x-4) = 1, we can apply the properties of exponents. Since any number raised to the power of zero is equal to 1, we can deduce that x - 4 must be equal to zero.

Now, to isolate x, we can add 4 to both sides of the equation:

x - 4 + 4 = 0 + 4

This simplifies to:

x = 4

Therefore, the solution to the equation 8^(x-4) = 1 is x = 4.

To solve the equation 8^(x-4) = 1 using mental math, we can follow these steps:

Step 1: Simplify the equation.
Given: 8^(x-4) = 1

Since any non-zero number raised to the power of 0 is always 1, we can simplify the equation further:
x - 4 = 0

Step 2: Solve for x.
Add 4 to both sides of the equation to isolate the variable:
x - 4 + 4 = 0 + 4
x = 4

Hence, the solution to the equation 8^(x-4) = 1 using mental math is x = 4.