Question

If 2^x-4 = 4^x-6 , then value of x is?​

Answer 1

Answer:
`x=1`

Explanation:

`2^x-4=4^x-6` is the equation that you've given us.

Now if we plot these two equations on the graph we notice there's an intersection at (1,-2). Therefore meaning that
`x=1`.

We can prove that by doing the following calculations to prove that both sides are equal to each other.

The left side of the equal sign:

Step 1: Write the equation down:

`2^x-4`

Step 2: Substitute x for the numerical value we found.

`2^1-4`

Step 3: Find the square of
`2^1`, which is itself, 2.

`2-4`

Step 4: Subtract 2 from 4. Which is a negative number, thus being -2.

`-2`

The right side of the equal sign:

Step 1: Write the equation down:

`4^x-6`

Step 2: Substitute x for the numerical value we found.

`4^1-6`

Step 3: Find the square of
`4^1`, which is itself, 4.

`4-6`

Step 4: Subtract 4 from 6. Which is a negative number, thus being -2.

`-2`

We know that
`x=1` because when substituting x with 1, we get -2 on both sides. Therefore making this statement true and valid.

`-2=-2`