Question

(1/25)^x=125 как это решить ?!

Answer 1

(1/25)^x=25^-x= 5^-2x=5^3
-2x=3
x=-1.5

Answer 2

To solve the equation (1/25)^x = 125, we need to get rid of the exponent in the base. We can do this by taking the logarithm of both sides of the equation. The most common logarithm used is the natural logarithm (base e), but any logarithm with a consistent base can be used. In this case, I will use the natural logarithm:

Step 1: Take the natural logarithm (ln) of both sides of the equation.

ln((1/25)^x) = ln(125)

Step 2: Use the properties of logarithms to bring down the exponent x.

x * ln(1/25) = ln(125)

Step 3: Calculate the logarithm values.

ln(1/25) can be simplified by using the property: ln(a/b) = ln(a) - ln(b)

x * (ln(1) - ln(25)) = ln(125)

Since ln(1) is 0, it simplifies to:

x * (-ln(25)) = ln(125)

Step 4: Divide both sides of the equation by -ln(25) to solve for x.

x = ln(125) / (-ln(25))

Now, use a calculator to find the approximate value of x:

x ≈ -1.8047

So, the approximate solution to the equation (1/25)^x = 125 is x ≈ -1.8047.