Certainly! Let's solve the equation step-by-step.
Given equation:
[tex]\[ 8^{x-4} = 8^{10} \][/tex]
### Step 1: Understanding the Equation
We have an equation in which both sides have the same base, which is 8.
### Step 2: Equating the Exponents
Because the bases are equal, in order for the equation to hold true, the exponents themselves must be equal. Therefore, we can set the exponents equal to each other:
[tex]\[ x - 4 = 10 \][/tex]
### Step 3: Solving for [tex]\( x \)[/tex]
Now, we need to isolate [tex]\( x \)[/tex] on one side of the equation. To do this, we add 4 to both sides of the equation:
[tex]\[ x - 4 + 4 = 10 + 4 \][/tex]
[tex]\[ x = 14 \][/tex]
### Conclusion
Thus, the value of [tex]\( x \)[/tex] that satisfies the given equation is:
[tex]\[ x = 14 \][/tex]
So, the solution to the equation [tex]\( 8^{x-4} = 8^{10} \)[/tex] is [tex]\( x = 14 \)[/tex].
