Solve the given equation 3=(243^(1)/(3))(3^(x)/(3)) x=square (Type an integer or a simplified fraction.)

Question

Answer 1

To solve the equation \(3 = (243^{\frac{1}{3}})(3^{\frac{x}{3}})\), we need to simplify both sides of the equation.First, let's simplify

:

Since

, we have:

Now, substitute this back into the original equation:

Next, use the property of exponents that states

:

Since the bases are the same, we can equate the exponents:

To solve for

, first combine the fractions on the right-hand side:

Multiply both sides by 3 to clear the fraction:

Finally, solve for

:

So, the solution to the equation is:

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