Solve for x 3^x=243

Problem

3^x=243

Solution

1. Identify the base of the exponential expression on the left side, which is 3

2. Rewrite the number on the right side as a power of 3 by performing prime factorization.

3. Calculate the powers of 3 3^1=3 3^2=9 3^3=27 3^4=81 and 3^5=243

4. Substitute 3^5 for 243 in the original equation.

3^x=3^5

5. Apply the property of equality for exponential functions, which states that if b^x=b^y and b>0,b≠1 then x=y

x=5

Final Answer

3^x=243⇒x=5

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