log5(5𝑥)=2 𝑥=

The equation is log5(5x) = 2. To solve for x, we need to convert the logarithmic equation into an exponential equation.

Step 1: Convert the logarithmic equation into an exponential equation. The base of the logarithm becomes the base of the exponent on the other side of the equation. The result of the logarithm becomes the exponent, and the argument of the logarithm (5x in this case) becomes the result on the other side of the equation.

So, the equation becomes: 5^2 = 5x

Step 2: Simplify the equation. 5^2 = 25, so the equation becomes: 25 = 5x

Step 3: Solve for x. To solve for x, divide both sides of the equation by 5.

25 / 5 = 5x / 5

This simplifies to: x = 5

So, the solution to the equation log5(5x) = 2 is x = 5.