Solving the Exponential Equation 6^{1-2x} = 5^x

Hi Tatiana, let's solve this exponential equation together. We need to find the value of x that satisfies six to the power of one minus two x equals five to the x.

Since the bases six and five are different and cannot be easily written with a common base, we should take the natural logarithm of both sides to bring the exponents down.

Using the power rule for logarithms, we can move the exponents to the front as multipliers.

Now, let's distribute the natural log of six on the left side of the equation.

Our goal is to isolate x. Let's move all terms containing x to the right side by adding two x times the log of six to both sides.

Now, we can factor out the common factor of x from the right side.