Solve 2^(-x)=3^(x+1) ?

To solve the equation 2^(-x) = 3^(x+1), we can rewrite it as:

1/(2^x) = 3^(x+1)

Now, we can rewrite 3^(x+1) as 3^x * 3^1 = 3 * 3^x = 3 * 3^x

So, the equation becomes:

1/(2^x) = 3 * 3^x

Now, we can rewrite 2^x as 2^x = 1/(2^(-x))

So, the equation becomes:

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^(-x)))

2^x = 1/(3 * 3^x)

Now, we can rewrite 3^x as 3^x = 1/(3^(-x))

So, the equation becomes:

2^x = 1/(3 * 1/(3^

2^(-x)=3^(x 1)
=> 2^(-x)=3^x
=> -x - log 2=x - log 3
=> -x = x - log 3/log 2
=> -x = x - 0.6309
=> -x = 0.6309x
=> -x - 0.6309x = 0
=> -1.6309x = 0
=> x = 0