Question

2^(4x-3)=0,125^(x+1)

Answer 1

2^4x-3=2^-3x-3
4x-3=-3x-3
4x=-3x
4x+3x=0
7x=0
x=0

Answer 2

The equation you've provided is:

2^(4x - 3) = 0.125^(x + 1)

Let's work on solving it step by step:

First, let's simplify 0.125^(x + 1). 0.125 is the same as 1/8, so we can rewrite it as:

(1/8)^(x + 1)

Now, remember that (a^b)^c = a^(b * c). Applying this property:

(1/8)^(x + 1) = 1^(x + 1) / 8^(x + 1) = 1 / 8^(x + 1)

So, the equation becomes:

2^(4x - 3) = 1 / 8^(x + 1)

Now, let's work on both sides of the equation:

On the left side, use the property that (a^b)^(c^d) = a^(b * c^d):

2^(4x - 3) = 2^(4x) * 2^(-3) = 16^x * 1/8

On the right side, simplify the expression:

1 / 8^(x + 1) = 1 / (8^x * 8) = 1 / (8^x) * 1/8

So the equation becomes:

16^x * 1/8 = 1 / (8^x) * 1/8

Now, both sides have a factor of 1/8, so we can cancel it out:

16^x = 1 / 8^x

Rewrite 16 as 2^4 and 8 as 2^3:

(2^4)^x = 1 / (2^3)^x

Simplify further:

2^(4x) = 1 / 2^(3x)

Apply the property that if a^(b) = a^(c), then b = c:

4x = -3x

Combine like terms:

7x = 0

Divide by 7:

x = 0

So, the solution to the equation is x = 0.