Answer: 1=x
The expression we have is:
[tex]6^5=6^x\times6^4[/tex]And we need to solve for x.
Step 1. Use the following rule of exponents:
[tex]A^m\times A^n=A^{m+n}[/tex]Using this rule on the right-hand side of the expression:
[tex]6^5=6^{x+4}^{}[/tex]Step 2. Since both sides of the expression have the same base (the same number 6 as the base of the exponent) that means that the exponent on the left side has to be equal to the exponent on the right side:
[tex]5=x+4[/tex]Step 3. Solve for x in the previous equation.
To solve for x, subtract 4 to both sides:
[tex]5-4=x+4-4[/tex]On the left side we get 1 and on the right side we get x:
[tex]1=x[/tex]Answer: 1=x
