Question

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

Answer 1

Answer: $x=1$

Step-by-step 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.

$-2=-2$