Certainly! Let's solve the equation step-by-step:
Given the equation:
[tex]\[ 8^{x-4} = 8^{10} \][/tex]
Since the __bases__ are equal (both are [tex]\(8\)[/tex]), the __exponents__ must also be equal.
Therefore, we can set the exponents equal to each other:
[tex]\[ x - 4 = 10 \][/tex]
Now, we solve for [tex]\(x\)[/tex]:
[tex]\[ x = 10 + 4 \][/tex]
Thus, the solution to the equation is:
[tex]\[ x = 14 \][/tex]
So, the completed solution is [tex]\( x = 14 \)[/tex].
