Question

Solve for x6^5=6^x × 6^4

Answer 1

Answer: 1=x

The expression we have is:

`6^5=6^x*6^4`

And we need to solve for x.

Step 1. Use the following rule of exponents:

`A^m* A^n=A^(m+n)`

Using this rule on the right-hand side of the expression:

`6^5=6^(x+4)^{}`

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:

`5=x+4`

Step 3. Solve for x in the previous equation.

To solve for x, subtract 4 to both sides:

`5-4=x+4-4`

On the left side we get 1 and on the right side we get x:

`1=x`

Answer: 1=x